AP Precalculus Flashcards: Equivalent Polynomial And Rational Expressions

Study Equivalent Polynomial And Rational Expressions in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Equivalent Polynomial And Rational Expressions

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QUESTION

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What is the standard form of a linear polynomial?

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ANSWER

$ax + b$ . The general form of a first-degree polynomial.

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What this deck covers

This deck focuses on Equivalent Polynomial And Rational Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

All flashcards

Flashcard 1: What is the standard form of a linear polynomial?

Answer: $ax + b$ . The general form of a first-degree polynomial.

Flashcard 2: What is the standard form of a quadratic polynomial?

Answer: $ax^2 + bx + c$ . The general form where $a \neq 0$ .

Flashcard 3: What is the quotient of $\frac{x^2 - 4}{x - 2}$ ?

Answer: $x + 2$ . Factor numerator: $\frac{(x+2)(x-2)}{x-2} = x+2$ .

Flashcard 4: Simplify $\frac{x^2 - 3x}{x - 3}$ .

Answer: $x$ . Factor numerator: $\frac{x(x-3)}{x-3} = x$ .

Flashcard 5: What is the expression for $(x - 3)^2$ ?

Answer: $x^2 - 6x + 9$ . Use $(a-b)^2 = a^2 - 2ab + b^2$ .

Flashcard 6: What is the sum of the roots of $x^2 - 4x + 4$ ?

Answer:

For $ax^2 + bx + c$ , sum of roots is $-\frac{b}{a}$ .

Flashcard 7: Rewrite $\frac{x^2 + 5x + 6}{x + 2}$ in simplest form.

Answer: $x + 3$ . Factor and cancel: $\frac{(x+2)(x+3)}{x+2} = x+3$ .

Flashcard 8: Which term refers to the highest degree term in a polynomial?

Answer: Leading term. The term with the highest degree in standard form.

Flashcard 9: Identify the expression equivalent to $\frac{x^3 - x}{x}$ .

Answer: $x^2 - 1$ . Factor and cancel: $\frac{x(x^2-1)}{x} = x^2-1$ .

Flashcard 10: What is the standard form of a quadratic polynomial?

Answer: $ax^2 + bx + c$ . The general form where $a \neq 0$ .

Flashcard 11: Identify the expression equivalent to $\frac{x^3 - x}{x}$ .

Answer: $x^2 - 1$ . Factor and cancel: $\frac{x(x^2-1)}{x} = x^2-1$ .

Flashcard 12: What is the expression for the cube of $(x + 2)$ ?

Answer: $x^3 + 6x^2 + 12x + 8$ . Use $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .

Flashcard 13: Simplify the expression $\frac{x^2 - 4x}{x}$ .

Answer: $x - 4$ . Factor out $x$ : $\frac{x(x-4)}{x} = x-4$ .

Flashcard 14: What is the expanded form of $(x + 1)^3$ ?

Answer: $x^3 + 3x^2 + 3x + 1$ . Use $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .

Flashcard 15: Simplify $\frac{x^2 - 3x}{x - 3}$ .

Answer: $x$ . Factor numerator: $\frac{x(x-3)}{x-3} = x$ .

Flashcard 16: What is the degree of the polynomial $4x^3 - 2x + 7$ ?

Answer:

The highest power of $x$ in the polynomial.

Flashcard 17: What is the standard form of a linear polynomial?

Answer: $ax + b$ . The general form of a first-degree polynomial.

Flashcard 18: Find the product of $(x + 1)$ and $(x - 1)$ .

Answer: $x^2 - 1$ . Difference of squares formula gives $x^2 - 1^2$ .

Flashcard 19: State the remainder when $x^3 + 3x^2 - x + 5$ is divided by $x - 1$ .

Answer:

By remainder theorem, substitute $x=1$ : $1+3-1+5=8$ .

Flashcard 20: Identify the expression equivalent to $\frac{x^2 + 2x}{x}$ .

Answer: $x + 2$ . Factor out $x$ : $\frac{x(x+2)}{x} = x+2$ .

Flashcard 21: State the discriminant of the quadratic $x^2 + 4x + 4$ .

Answer:

For perfect square, discriminant $b^2 - 4ac = 0$ .

Flashcard 22: What is the binomial theorem?

Answer: $(a + b)^n = \text{sum of terms } C(n, k)a^{n-k}b^k$ . Expands $(a+b)^n$ using combinations and powers.

Flashcard 23: Factor $x^2 + 6x + 9$ .

Answer: $(x + 3)^2$ . Perfect square trinomial: $a^2 + 2ab + b^2 = (a+b)^2$ .

Flashcard 24: Convert $\frac{3x + 6}{x + 2}$ to simplest form.

Answer:

Factor and cancel: $\frac{3(x+2)}{x+2} = 3$ .

Flashcard 25: What is the expression for the cube of $(x + 2)$ ?

Answer: $x^3 + 6x^2 + 12x + 8$ . Use $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .

Flashcard 26: Simplify the expression $\frac{x^2 - 4x}{x}$ .

Answer: $x - 4$ . Factor out $x$ : $\frac{x(x-4)}{x} = x-4$ .

Flashcard 27: Express $x^3 - 27$ as a product of factors.

Answer: $(x - 3)(x^2 + 3x + 9)$ . Difference of cubes: $a^3 - b^3 = (a-b)(a^2+ab+b^2)$ .

Flashcard 28: What is the binomial theorem?

Answer: $(a + b)^n = \text{sum of terms } C(n, k)a^{n-k}b^k$ . Expands $(a + b)^n$ using combinations and powers.

Flashcard 29: What is the factored form of $x^2 - 9$ ?

Answer: $(x - 3)(x + 3)$ . Difference of squares: $a^2 - b^2 = (a-b)(a+b)$ .

Flashcard 30: State the expression for the difference of cubes $a^3 - b^3$ .

Answer: $(a - b)(a^2 + ab + b^2)$ . The factorization formula for $a^3 - b^3$ .

Flashcard 31: Identify the leading coefficient in $5x^4 - 3x^2 + x$ .

Answer:

The coefficient of the highest degree term.

Flashcard 32: What is the expression for the sum of $2x^2 + 3x$ and $x^2 - x$ ?

Answer: $3x^2 + 2x$ . Combine like terms: $(2+1)x^2 + (3-1)x = 3x^2 + 2x$ .

Flashcard 33: Simplify the expression $2x(x^2 - 3x + 4)$ .

Answer: $2x^3 - 6x^2 + 8x$ . Distribute $2x$ to each term inside parentheses.

Flashcard 34: Identify the expression equivalent to $\frac{x^2 + 2x}{x}$ .

Answer: $x + 2$ . Factor out $x$ : $\frac{x(x+2)}{x} = x+2$ .

Flashcard 35: What does it mean for a polynomial to be monic?

Answer: Leading coefficient is 1. The coefficient of the highest degree term equals 1.

Flashcard 36: Factor $x^2 + 6x + 9$ .

Answer: $(x + 3)^2$ . Perfect square trinomial: $a^2 + 2ab + b^2 = (a+b)^2$ .

Flashcard 37: What is the expression for the difference between $x^2 + 4x$ and $2x^2 + x$ ?

Answer: $-x^2 + 3x$ . $(x^2 + 4x) - (2x^2 + x) = -x^2 + 3x$ .

Flashcard 38: What is the common denominator of $\frac{1}{x}$ and $\frac{1}{x^2}$ ?

Answer: $x^2$ . Use the highest power of $x$ in both denominators.

Flashcard 39: What is the polynomial remainder theorem?

Answer: Remainder of $f(x)$ divided by $x - a$ is $f(a)$ . Substitute $x=a$ into $f(x)$ to find remainder.

Flashcard 40: State the expression for the difference of cubes $a^3 - b^3$ .

Answer: $(a - b)(a^2 + ab + b^2)$ . The factorization formula for $a^3 - b^3$ .

Flashcard 41: What is the degree of the polynomial $4x^3 - 2x + 7$ ?

Answer: $3$ . The highest power of $x$ in the polynomial.

Flashcard 42: What is the polynomial remainder theorem?

Answer: Remainder of $f(x)$ divided by $x - a$ is $f(a)$ . Substitute $x=a$ into $f(x)$ to find remainder.

Flashcard 43: Express $3x^2 - 12$ as a product of its factors.

Answer: $3(x^2 - 4)$ . Factor out common factor 3 first.

Flashcard 44: What is the expression for the square of $(x + 2)$ ?

Answer: $x^2 + 4x + 4$ . Use $(a+b)^2 = a^2 + 2ab + b^2$ .

Flashcard 45: State the remainder when $x^3 + 3x^2 - x + 5$ is divided by $x - 1$ .

Answer:

By remainder theorem, substitute $x=1$ : $1+3-1+5=8$ .

Flashcard 46: What is the product of the roots of $x^2 - 5x + 6$ ?

Answer:

For $ax^2 + bx + c$ , product of roots is $\frac{c}{a}$ .

Flashcard 47: State the zeroes of the polynomial $x^2 - 5x + 6$ .

Answer: 2, 3. Factor as $(x-2)(x-3)$ and set each factor to zero.

Flashcard 48: What is the term for a polynomial with three terms?

Answer: Trinomial. A polynomial with exactly three terms.

Flashcard 49: What is the expression for the square of $(x + 2)$ ?

Answer: $x^2 + 4x + 4$ . Use $(a+b)^2 = a^2 + 2ab + b^2$ .

Flashcard 50: Simplify the expression $\frac{x^2 - 9}{x + 3}$ .

Answer: $x - 3$ . Factor numerator: $\frac{(x+3)(x-3)}{x+3} = x-3$ .

Flashcard 51: Simplify the expression $\frac{x^2 - 9}{x + 3}$ .

Answer: $x - 3$ . Factor numerator: $\frac{(x+3)(x-3)}{x+3} = x-3$ .

Flashcard 52: What is the expression for the difference between $x^2 + 4x$ and $2x^2 + x$ ?

Answer: $-x^2 + 3x$ . $(x^2 + 4x) - (2x^2 + x) = -x^2 + 3x$

Flashcard 53: Rewrite $\frac{x^2 + 5x + 6}{x + 2}$ in simplest form.

Answer: $x + 3$ . Factor and cancel: $\frac{(x+2)(x+3)}{x+2} = x+3$ .

Flashcard 54: What does it mean for a polynomial to be monic?

Answer: Leading coefficient is 1. The coefficient of the highest degree term equals 1.

Flashcard 55: What is the greatest common factor of $6x^2 + 9x$ ?

Answer: 3x. Factor out the GCF: $3x(2x + 3)$ .

Flashcard 56: Express $3x^2 - 12$ as a product of its factors.

Answer: $3(x^2 - 4)$ . Factor out common factor 3 first.

Flashcard 57: What is the quotient of $\frac{x^2 - 4}{x - 2}$ ?

Answer: $x + 2$ . Factor numerator: $\frac{(x+2)(x-2)}{x-2} = x+2$ .

Flashcard 58: Convert $\frac{3x + 6}{x + 2}$ to simplest form.

Answer:

Factor and cancel: $\frac{3(x+2)}{x+2} = 3$ .

Flashcard 59: Express $x^3 - 27$ as a product of factors.

Answer: $(x - 3)(x^2 + 3x + 9)$ . Difference of cubes: $a^3 - b^3 = (a-b)(a^2+ab+b^2)$ .

Flashcard 60: Identify the leading coefficient in $5x^4 - 3x^2 + x$ .

Answer:

The coefficient of the highest degree term.

Flashcard 61: What is the expression for $(x - 3)^2$ ?

Answer: $x^2 - 6x + 9$ . Use $(a-b)^2 = a^2 - 2ab + b^2$ .

Flashcard 62: What is the common denominator of $\frac{1}{x}$ and $\frac{1}{x^2}$ ?

Answer: $x^2$ . Use the highest power of $x$ in both denominators.

Flashcard 63: State the discriminant of the quadratic $x^2 + 4x + 4$ .

Answer:

For perfect square, discriminant $b^2 - 4ac = 0$ .

Flashcard 64: Which term refers to the highest degree term in a polynomial?

Answer: Leading term. The term with the highest degree in standard form.

Flashcard 65: What is the expression for the sum of $2x^2 + 3x$ and $x^2 - x$ ?

Answer: $3x^2 + 2x$ . Combine like terms: $(2+1)x^2 + (3-1)x = 3x^2 + 2x$ .

Flashcard 66: What is the expanded form of $(x + 1)^3$ ?

Answer: $x^3 + 3x^2 + 3x + 1$ . Use $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .

Flashcard 67: State the zeroes of the polynomial $x^2 - 5x + 6$ .

Answer: 2, 3. Factor as $(x-2)(x-3)$ and set each factor to zero.

Flashcard 68: Convert $f(x) = (x - 2)(x + 3)$ to standard form.

Answer: $x^2 + x - 6$ . Use FOIL: $(x-2)(x+3) = x^2 + 3x - 2x - 6$ .

Flashcard 69: What is the term for a polynomial with three terms?

Answer: Trinomial. A polynomial with exactly three terms.

AP Precalculus Flashcards: Equivalent Polynomial And Rational Expressions

Equivalent Polynomial And Rational Expressions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What is the standard form of a linear polynomial?

Flashcard 2: What is the standard form of a quadratic polynomial?

Flashcard 3: What is the quotient of x2−4x−2\frac{x^2 - 4}{x - 2}x−2x2−4​?

Flashcard 4: Simplify x2−3xx−3\frac{x^2 - 3x}{x - 3}x−3x2−3x​.

Flashcard 5: What is the expression for (x−3)2(x - 3)^2(x−3)2?

Flashcard 6: What is the sum of the roots of x2−4x+4x^2 - 4x + 4x2−4x+4?

Flashcard 7: Rewrite x2+5x+6x+2\frac{x^2 + 5x + 6}{x + 2}x+2x2+5x+6​ in simplest form.

Flashcard 8: Which term refers to the highest degree term in a polynomial?

Flashcard 9: Identify the expression equivalent to x3−xx\frac{x^3 - x}{x}xx3−x​.

Flashcard 10: What is the standard form of a quadratic polynomial?

Flashcard 11: Identify the expression equivalent to x3−xx\frac{x^3 - x}{x}xx3−x​.

Flashcard 12: What is the expression for the cube of (x+2)(x + 2)(x+2)?

Flashcard 13: Simplify the expression x2−4xx\frac{x^2 - 4x}{x}xx2−4x​.

Flashcard 14: What is the expanded form of (x+1)3(x + 1)^3(x+1)3?

Flashcard 15: Simplify x2−3xx−3\frac{x^2 - 3x}{x - 3}x−3x2−3x​.

Flashcard 16: What is the degree of the polynomial 4x3−2x+74x^3 - 2x + 74x3−2x+7?

Flashcard 17: What is the standard form of a linear polynomial?

Flashcard 18: Find the product of (x+1)(x + 1)(x+1) and (x−1)(x - 1)(x−1).

Flashcard 19: State the remainder when x3+3x2−x+5x^3 + 3x^2 - x + 5x3+3x2−x+5 is divided by x−1x - 1x−1.

Flashcard 20: Identify the expression equivalent to x2+2xx\frac{x^2 + 2x}{x}xx2+2x​.

Flashcard 21: State the discriminant of the quadratic x2+4x+4x^2 + 4x + 4x2+4x+4.

Flashcard 22: What is the binomial theorem?

Flashcard 23: Factor x2+6x+9x^2 + 6x + 9x2+6x+9.

Flashcard 24: Convert 3x+6x+2\frac{3x + 6}{x + 2}x+23x+6​ to simplest form.

Flashcard 25: What is the expression for the cube of (x+2)(x + 2)(x+2)?

Flashcard 26: Simplify the expression x2−4xx\frac{x^2 - 4x}{x}xx2−4x​.

Flashcard 27: Express x3−27x^3 - 27x3−27 as a product of factors.

Flashcard 28: What is the binomial theorem?

Flashcard 29: What is the factored form of x2−9x^2 - 9x2−9?

Flashcard 30: State the expression for the difference of cubes a3−b3a^3 - b^3a3−b3.

Flashcard 31: Identify the leading coefficient in 5x4−3x2+x5x^4 - 3x^2 + x5x4−3x2+x.

Flashcard 32: What is the expression for the sum of 2x2+3x2x^2 + 3x2x2+3x and x2−xx^2 - xx2−x?

Flashcard 33: Simplify the expression 2x(x2−3x+4)2x(x^2 - 3x + 4)2x(x2−3x+4).

Flashcard 34: Identify the expression equivalent to x2+2xx\frac{x^2 + 2x}{x}xx2+2x​.

Flashcard 35: What does it mean for a polynomial to be monic?

Flashcard 36: Factor x2+6x+9x^2 + 6x + 9x2+6x+9.

Flashcard 37: What is the expression for the difference between x2+4xx^2 + 4xx2+4x and 2x2+x2x^2 + x2x2+x?

Flashcard 38: What is the common denominator of 1x\frac{1}{x}x1​ and 1x2\frac{1}{x^2}x21​?

Flashcard 39: What is the polynomial remainder theorem?

Flashcard 40: State the expression for the difference of cubes a3−b3a^3 - b^3a3−b3.

Flashcard 41: What is the degree of the polynomial 4x3−2x+74x^3 - 2x + 74x3−2x+7?

Flashcard 42: What is the polynomial remainder theorem?

Flashcard 43: Express 3x2−123x^2 - 123x2−12 as a product of its factors.

Flashcard 44: What is the expression for the square of (x+2)(x + 2)(x+2)?

Flashcard 45: State the remainder when x3+3x2−x+5x^3 + 3x^2 - x + 5x3+3x2−x+5 is divided by x−1x - 1x−1.

Flashcard 46: What is the product of the roots of x2−5x+6x^2 - 5x + 6x2−5x+6?

Flashcard 47: State the zeroes of the polynomial x2−5x+6x^2 - 5x + 6x2−5x+6.

Flashcard 48: What is the term for a polynomial with three terms?

Flashcard 49: What is the expression for the square of (x+2)(x + 2)(x+2)?

Flashcard 50: Simplify the expression x2−9x+3\frac{x^2 - 9}{x + 3}x+3x2−9​.

Flashcard 51: Simplify the expression x2−9x+3\frac{x^2 - 9}{x + 3}x+3x2−9​.

Flashcard 52: What is the expression for the difference between x2+4xx^2 + 4xx2+4x and 2x2+x2x^2 + x2x2+x?

Flashcard 53: Rewrite x2+5x+6x+2\frac{x^2 + 5x + 6}{x + 2}x+2x2+5x+6​ in simplest form.

Flashcard 54: What does it mean for a polynomial to be monic?

Flashcard 55: What is the greatest common factor of 6x2+9x6x^2 + 9x6x2+9x?

Flashcard 56: Express 3x2−123x^2 - 123x2−12 as a product of its factors.

Flashcard 57: What is the quotient of x2−4x−2\frac{x^2 - 4}{x - 2}x−2x2−4​?

Flashcard 58: Convert 3x+6x+2\frac{3x + 6}{x + 2}x+23x+6​ to simplest form.

Flashcard 59: Express x3−27x^3 - 27x3−27 as a product of factors.

Flashcard 60: Identify the leading coefficient in 5x4−3x2+x5x^4 - 3x^2 + x5x4−3x2+x.

Flashcard 61: What is the expression for (x−3)2(x - 3)^2(x−3)2?

Flashcard 62: What is the common denominator of 1x\frac{1}{x}x1​ and 1x2\frac{1}{x^2}x21​?

Flashcard 63: State the discriminant of the quadratic x2+4x+4x^2 + 4x + 4x2+4x+4.

Flashcard 64: Which term refers to the highest degree term in a polynomial?

Flashcard 65: What is the expression for the sum of 2x2+3x2x^2 + 3x2x2+3x and x2−xx^2 - xx2−x?

Flashcard 66: What is the expanded form of (x+1)3(x + 1)^3(x+1)3?

Flashcard 67: State the zeroes of the polynomial x2−5x+6x^2 - 5x + 6x2−5x+6.

Flashcard 68: Convert f(x)=(x−2)(x+3)f(x) = (x - 2)(x + 3)f(x)=(x−2)(x+3) to standard form.

Flashcard 69: What is the term for a polynomial with three terms?

Flashcard 3: What is the quotient of $\frac{x^2 - 4}{x - 2}$ ?

Flashcard 4: Simplify $\frac{x^2 - 3x}{x - 3}$ .

Flashcard 5: What is the expression for $(x - 3)^2$ ?

Flashcard 6: What is the sum of the roots of $x^2 - 4x + 4$ ?

Flashcard 7: Rewrite $\frac{x^2 + 5x + 6}{x + 2}$ in simplest form.

Flashcard 9: Identify the expression equivalent to $\frac{x^3 - x}{x}$ .

Flashcard 11: Identify the expression equivalent to $\frac{x^3 - x}{x}$ .

Flashcard 12: What is the expression for the cube of $(x + 2)$ ?

Flashcard 13: Simplify the expression $\frac{x^2 - 4x}{x}$ .

Flashcard 14: What is the expanded form of $(x + 1)^3$ ?

Flashcard 15: Simplify $\frac{x^2 - 3x}{x - 3}$ .

Flashcard 16: What is the degree of the polynomial $4x^3 - 2x + 7$ ?

Flashcard 18: Find the product of $(x + 1)$ and $(x - 1)$ .

Flashcard 19: State the remainder when $x^3 + 3x^2 - x + 5$ is divided by $x - 1$ .

Flashcard 20: Identify the expression equivalent to $\frac{x^2 + 2x}{x}$ .

Flashcard 21: State the discriminant of the quadratic $x^2 + 4x + 4$ .

Flashcard 23: Factor $x^2 + 6x + 9$ .

Flashcard 24: Convert $\frac{3x + 6}{x + 2}$ to simplest form.

Flashcard 25: What is the expression for the cube of $(x + 2)$ ?

Flashcard 26: Simplify the expression $\frac{x^2 - 4x}{x}$ .

Flashcard 27: Express $x^3 - 27$ as a product of factors.

Flashcard 29: What is the factored form of $x^2 - 9$ ?

Flashcard 30: State the expression for the difference of cubes $a^3 - b^3$ .

Flashcard 31: Identify the leading coefficient in $5x^4 - 3x^2 + x$ .

Flashcard 32: What is the expression for the sum of $2x^2 + 3x$ and $x^2 - x$ ?

Flashcard 33: Simplify the expression $2x(x^2 - 3x + 4)$ .

Flashcard 34: Identify the expression equivalent to $\frac{x^2 + 2x}{x}$ .

Flashcard 36: Factor $x^2 + 6x + 9$ .

Flashcard 37: What is the expression for the difference between $x^2 + 4x$ and $2x^2 + x$ ?

Flashcard 38: What is the common denominator of $\frac{1}{x}$ and $\frac{1}{x^2}$ ?

Flashcard 40: State the expression for the difference of cubes $a^3 - b^3$ .

Flashcard 41: What is the degree of the polynomial $4x^3 - 2x + 7$ ?

Flashcard 43: Express $3x^2 - 12$ as a product of its factors.

Flashcard 44: What is the expression for the square of $(x + 2)$ ?

Flashcard 45: State the remainder when $x^3 + 3x^2 - x + 5$ is divided by $x - 1$ .

Flashcard 46: What is the product of the roots of $x^2 - 5x + 6$ ?

Flashcard 47: State the zeroes of the polynomial $x^2 - 5x + 6$ .

Flashcard 49: What is the expression for the square of $(x + 2)$ ?

Flashcard 50: Simplify the expression $\frac{x^2 - 9}{x + 3}$ .

Flashcard 51: Simplify the expression $\frac{x^2 - 9}{x + 3}$ .

Flashcard 52: What is the expression for the difference between $x^2 + 4x$ and $2x^2 + x$ ?

Flashcard 53: Rewrite $\frac{x^2 + 5x + 6}{x + 2}$ in simplest form.

Flashcard 55: What is the greatest common factor of $6x^2 + 9x$ ?

Flashcard 56: Express $3x^2 - 12$ as a product of its factors.

Flashcard 57: What is the quotient of $\frac{x^2 - 4}{x - 2}$ ?

Flashcard 58: Convert $\frac{3x + 6}{x + 2}$ to simplest form.

Flashcard 59: Express $x^3 - 27$ as a product of factors.

Flashcard 60: Identify the leading coefficient in $5x^4 - 3x^2 + x$ .

Flashcard 61: What is the expression for $(x - 3)^2$ ?

Flashcard 62: What is the common denominator of $\frac{1}{x}$ and $\frac{1}{x^2}$ ?

Flashcard 63: State the discriminant of the quadratic $x^2 + 4x + 4$ .

Flashcard 65: What is the expression for the sum of $2x^2 + 3x$ and $x^2 - x$ ?

Flashcard 66: What is the expanded form of $(x + 1)^3$ ?

Flashcard 67: State the zeroes of the polynomial $x^2 - 5x + 6$ .

Flashcard 68: Convert $f(x) = (x - 2)(x + 3)$ to standard form.