Algebra 2 Flashcards: Terms Factors And Coefficients

What this deck covers

This deck focuses on Terms Factors And Coefficients, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

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.

Flashcard 1: What is the leading coefficient of the polynomial $6x^4-2x+3$?

Answer: $6$. The coefficient of the highest degree term.

Flashcard 2: What is the coefficient of $x^2$ in the expanded form of $x(x+2)$?

Answer: $1$. After expanding: $x^2 + 2x$, coefficient is $1$.

Flashcard 3: Identify the numerical coefficient in the term -rac{3}{5}ab^2.

Answer: -rac{3}{5}. The fraction multiplying the variable part.

Flashcard 4: What does it mean for an expression to be a sum of terms?

Answer: It is written using addition/subtraction between terms. Each term is connected by addition or subtraction.

Flashcard 5: Identify the constant term in the polynomial $-8x^2+0x+11$.

Answer: $11$. The term with no variables, coefficient of $x^0$.

Flashcard 6: Identify the factors of the expression $x^2+5x$ as a product.

Answer: $x(x+5)$. Common factor $x$ factored out.

Flashcard 7: Identify the top-level terms in the expression $4x-(2x-7)$.

Answer: $4x$ and $-(2x-7)$. The subtraction creates two main terms.

Flashcard 8: What is the coefficient of $x^2$ in the expression $3-2x^2+9x^5$?

Answer: $-2$. The number multiplying $x^2$ in that term.

Flashcard 9: Identify the coefficient of $x$ in the expression $x(x+2)$ when viewed as $x ext{ times }(x+2)$.

Answer: $1$. The coefficient of $x$ when treating this as multiplication.

Flashcard 10: Which expression shows $-6x^2y$ as a product of a coefficient and variable factors?

Answer: $-6 imes x^2 imes y$. Shows coefficient separated from variable factors.

Flashcard 11: What is the coefficient of $x^3$ in the expression $-x^3+2x^2-x+8$?

Answer: $-1$. The negative sign indicates coefficient $-1$.

Flashcard 12: What is the coefficient of $x$ in the expanded form of $x(x+2)$?

Answer: $2$. After expanding: $x^2 + 2x$, coefficient is $2$.

Flashcard 13: Identify the factors of the term $4x^2y$ written as a product of three factors.

Answer: $4 imes x^2 imes y$. Breaking down into coefficient, $x^2$, and $y$.

Flashcard 14: What is the greatest common factor of the terms $6x^2$ and $9x$?

Answer: $3x$. Factor out the highest power common to both terms.

Flashcard 15: What is a factor in an algebraic expression?

Answer: A quantity multiplied by other quantities. Factors are multiplied together to form a product.

Flashcard 16: Identify the number of terms in the expression $7(x+1)$.

Answer: $1$. The parentheses make this one complete term.

Flashcard 17: What is the implied coefficient of $x$ in the term $x$?

Answer: $1$. When no coefficient is written, it equals $1$.

Flashcard 18: What is a coefficient of a variable term?

Answer: The numerical factor multiplying the variable part. The number multiplying the variables in a term.

Flashcard 19: Identify the numerical coefficient in the term $-\frac{3}{5}ab^2$.

Answer: $-\frac{3}{5}$. The fraction multiplying the variable part.

Flashcard 20: What is the implied coefficient of $-x$ in the term $-x$?

Answer: $-1$. The negative sign indicates coefficient $-1$.

Flashcard 21: Identify the coefficient of $(x-4)$ in the expression $3(x-4)+2$.

Answer: $3$. The number multiplying the parenthetical expression.

Flashcard 22: What is the leading term of the polynomial $-3x^5+4x^2-1$?

Answer: $-3x^5$. The term with the highest degree.

Flashcard 23: Identify the coefficient of $x^2y$ in the term $9x^2y$.

Answer: $9$. The number multiplying the entire variable part.

Flashcard 24: Identify the factors of the term $-14x^3$.

Answer: $-14$ and $x^3$. The coefficient $-14$ and variable part $x^3$.

Flashcard 25: Identify the coefficient of $x^2y^3$ in the term $x^2y^3$.

Answer: $1$. When no number is shown, coefficient is $1$.

Flashcard 26: Identify the coefficient of $x^2$ in the expression $-4x^2+9x-1$.

Answer: $-4$. The number multiplying $x^2$ in the term.

Flashcard 27: Identify the factors in the term $-2(x+3)$.

Answer: $-2$ and $(x+3)$. The coefficient and the parenthetical expression.

Flashcard 28: Identify the constant term in the simplified form of $-(x-5)$.

Answer: $5$. From distributing: $-x + 5$, the constant is $5$.

Flashcard 29: Identify the coefficient of $x$ in the expression $-9x+4$.

Answer: $-9$. The number directly multiplying $x$.

Flashcard 30: Which part of $8(x-1)(x+2)$ is the coefficient of the product $(x-1)(x+2)$?

Answer: $8$. The number multiplying the entire parenthetical expression.

Flashcard 31: Identify the coefficient of $x$ in the expression $-(x-5)$ after simplifying.

Answer: $-1$. Distribute the negative: $-x + 5$, so coefficient is $-1$.

Flashcard 32: What is the degree of the monomial $7x^3y^2$?

Answer: $5$. Add the exponents: $3 + 2 = 5$.

Flashcard 33: Identify the factors of the expression $x^2-9$ as a product.

Answer: $(x-3)(x+3)$. Factored form of the difference of squares.

Flashcard 34: Identify the coefficient of $ab$ in the expression $-7ab+3a-2b$.

Answer: $-7$. The number multiplying both variables $a$ and $b$.

Flashcard 35: Identify the terms in the expression $3x^2-5x+7$.

Answer: $3x^2$, $-5x$, $7$. Terms are separated by plus and minus signs.

Flashcard 36: Identify the variable factors in the term $6x^2y^3$.

Answer: $x^2$ and $y^3$. The parts containing variables with their exponents.

Flashcard 37: Identify the terms in the expression $2(a-3)+5$.

Answer: $2(a-3)$ and $5$. Each part separated by addition at the top level.

Flashcard 38: Identify the coefficient of $x^2$ in the expression $x^2-6x+1$.

Answer: $1$. When no number is shown, the coefficient is $1$.

Flashcard 39: What is a constant term in an expression?

Answer: A term with no variables. It contains only numbers, no variable parts.

Flashcard 40: Identify the coefficient of $x^0$ in the polynomial $4x^2-3x+9$.

Answer: $9$. The constant term is the coefficient of $x^0$.

Flashcard 41: Identify the coefficient of $x$ in the expression rac{1}{2}x-3.

Answer: rac{1}{2}. The fraction multiplying the variable $x$.

Flashcard 42: Identify the coefficient of $x^2y^3$ in the term $-x^2y^3$.

Answer: $-1$. The negative sign indicates coefficient $-1$.

Flashcard 43: Identify the constant factor in the term rac{7}{3}x^4.

Answer: rac{7}{3}. The fractional coefficient of the variable part.

Flashcard 44: Identify the number of terms in the expression $5x^2y-2y+9$.

Answer: $3$. Count parts separated by plus or minus signs.

Flashcard 45: Identify the constant factor in the term $15mn$.

Answer: $15$. The numerical part of the term.

Flashcard 46: Identify the constant term in the expression $12-3x+2x^2$.

Answer: $12$. The term with no variables attached.

Flashcard 47: Identify the terms in the expression $-5(a+b)+2$.

Answer: $-5(a+b)$ and $2$. Two parts separated by addition.

Flashcard 48: Identify the coefficient of $y$ in the expression $4x+3y-2$.

Answer: $3$. The number multiplying the variable $y$.

Flashcard 49: What is a term in an algebraic expression?

Answer: A part separated by $+$ or $-$ at the top level. Terms are separated by addition or subtraction operations.

Flashcard 50: Identify the variable part of the term $-12x^3y$.

Answer: $x^3y$. All the variable parts with their exponents.

Flashcard 51: What is the meaning of the coefficient in the term $kx$ when $k$ is a constant?

Answer: $k$ is the number multiplying $x$. It represents how many times $x$ is counted.