ISEE Upper Level Mathematics Achievement Flashcards: Factoring Expressions

What this deck covers

This deck focuses on Factoring Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Mathematics Achievement.

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 factored form of $x^2 + 6x - 16$ over the integers?

Answer: $(x+8)(x-2)$. Find two integers that multiply to -16 and add to 6, yielding factors $(x + 8)$ and $(x - 2)$.

Flashcard 2: What is the greatest common factor (GCF) of $12x^3y^2$ and $18x^2y^5$?

Answer: $6x^2y^2$. The GCF is found by taking the lowest powers of common prime factors (2 and 3) and variables ($x^2$ and $y^2$) from both terms.

Flashcard 3: Identify the factored form of $4x^2 - 25$.

Answer: $(2x-5)(2x+5)$. Recognize $4x^2 - 25$ as a difference of squares, $(2x)^2 - 5^2 = (2x - 5)(2x + 5)$.

Flashcard 4: Identify the factored form of $9x^2 - 12x + 4$ as a perfect square.

Answer: $(3x-2)^2$. The trinomial $9x^2 - 12x + 4$ matches the perfect square form $(3x - 2)^2$.

Flashcard 5: Identify the factored form of $2x^2 - 18$ as completely as possible.

Answer: $2(x-3)(x+3)$. First factor out the GCF of 2, then factor the remaining difference of squares $x^2 - 9$.

Flashcard 6: What is the factored form of $2x^2 + 7x + 3$?

Answer: $(2x+1)(x+3)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(2x + 1)(x + 3)$.

Flashcard 7: What is the factored form of $x^2 + 10x + 25$ as a perfect square trinomial?

Answer: $(x+5)^2$. The trinomial $x^2 + 10x + 25$ is a perfect square since it matches $(x + 5)^2$.

Flashcard 8: What is the factored form of $x^2 - x - 12$ over the integers?

Answer: $(x-4)(x+3)$. Find two integers that multiply to -12 and add to -1, yielding factors $(x - 4)$ and $(x + 3)$.

Flashcard 9: Identify the factored form of $x^2 + 2x - 35$ over the integers.

Answer: $(x+7)(x-5)$. Find two integers that multiply to -35 and add to 2, yielding factors $(x + 7)$ and $(x - 5)$.

Flashcard 10: Identify the factored form of $8x^2 - 12x$ using the GCF.

Answer: $4x(2x-3)$. Factor out the GCF of $4x$ from both terms, leaving $2x - 3$ inside the parentheses.

Flashcard 11: State the identity for factoring a sum of cubes.

Answer: $a^3+b^3=(a+b)(a^2-ab+b^2)$. The sum of cubes identity factors $a^3 + b^3$ into $(a + b)(a^2 - ab + b^2)$.

Flashcard 12: Identify the factored form of $5x^2 - 20x$ using the GCF.

Answer: $5x(x-4)$. Factor out the GCF of $5x$ from both terms, leaving $x - 4$ inside the parentheses.

Flashcard 13: State the identity for factoring a difference of cubes.

Answer: $a^3-b^3=(a-b)(a^2+ab+b^2)$. The difference of cubes identity factors $a^3 - b^3$ into $(a - b)(a^2 + ab + b^2)$.

Flashcard 14: State the identity for factoring a difference of squares.

Answer: $a^2-b^2=(a-b)(a+b)$. The difference of squares identity factors $a^2 - b^2$ into $(a - b)(a + b)$.

Flashcard 15: What is the factored form of $3x^2 - 11x - 4$?

Answer: $(3x+1)(x-4)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(3x + 1)(x - 4)$.

Flashcard 16: What is the factored form of $x^2 - 16x + 64$ as a perfect square trinomial?

Answer: $(x-8)^2$. The trinomial $x^2 - 16x + 64$ is a perfect square since it matches $(x - 8)^2$.

Flashcard 17: State the identity for factoring a perfect square trinomial $a^2-2ab+b^2$.

Answer: $a^2-2ab+b^2=(a-b)^2$. The perfect square trinomial identity factors $a^2 - 2ab + b^2$ as $(a - b)^2$.

Flashcard 18: What is the factored form of $x^2 - 9$ as a difference of squares?

Answer: $(x-3)(x+3)$. Recognize $x^2 - 9$ as a difference of squares, where $x^2 - 3^2 = (x - 3)(x + 3)$.

Flashcard 19: Identify the factored form of $6x^2 - 54$ by factoring out the GCF first.

Answer: $6(x-3)(x+3)$. First factor out the GCF of 6, then factor the remaining difference of squares $x^2 - 9$.

Flashcard 20: State the identity for factoring a perfect square trinomial $a^2+2ab+b^2$.

Answer: $a^2+2ab+b^2=(a+b)^2$. The perfect square trinomial identity factors $a^2 + 2ab + b^2$ as $(a + b)^2$.

Flashcard 21: What is the factored form of $ax+ay+bx+by$ by factoring by grouping?

Answer: $(a+b)(x+y)$. Group terms as $(ax + ay) + (bx + by) = a(x + y) + b(x + y)$, then factor out the common binomial.

Flashcard 22: What is the factored form of $x^2 + 7x + 12$ over the integers?

Answer: $(x+3)(x+4)$. Find two integers that multiply to 12 and add to 7, yielding factors $(x + 3)$ and $(x + 4)$.