Factoring Expressions - ISEE Upper Level: Mathematics Achievement
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Identify the factored form of $x^2 + 2x - 35$ over the integers.
Identify the factored form of $x^2 + 2x - 35$ over the integers.
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$(x+7)(x-5)$. Find two integers that multiply to -35 and add to 2, yielding factors $(x + 7)$ and $(x - 5)$.
$(x+7)(x-5)$. Find two integers that multiply to -35 and add to 2, yielding factors $(x + 7)$ and $(x - 5)$.
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What is the factored form of $x^2 + 7x + 12$ over the integers?
What is the factored form of $x^2 + 7x + 12$ over the integers?
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$(x+3)(x+4)$. Find two integers that multiply to 12 and add to 7, yielding factors $(x + 3)$ and $(x + 4)$.
$(x+3)(x+4)$. Find two integers that multiply to 12 and add to 7, yielding factors $(x + 3)$ and $(x + 4)$.
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What is the factored form of $x^2 - x - 12$ over the integers?
What is the factored form of $x^2 - x - 12$ over the integers?
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$(x-4)(x+3)$. Find two integers that multiply to -12 and add to -1, yielding factors $(x - 4)$ and $(x + 3)$.
$(x-4)(x+3)$. Find two integers that multiply to -12 and add to -1, yielding factors $(x - 4)$ and $(x + 3)$.
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State the identity for factoring a perfect square trinomial $a^2+2ab+b^2$.
State the identity for factoring a perfect square trinomial $a^2+2ab+b^2$.
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$a^2+2ab+b^2=(a+b)^2$. The perfect square trinomial identity factors $a^2 + 2ab + b^2$ as $(a + b)^2$.
$a^2+2ab+b^2=(a+b)^2$. The perfect square trinomial identity factors $a^2 + 2ab + b^2$ as $(a + b)^2$.
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What is the factored form of $x^2 + 10x + 25$ as a perfect square trinomial?
What is the factored form of $x^2 + 10x + 25$ as a perfect square trinomial?
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$(x+5)^2$. The trinomial $x^2 + 10x + 25$ is a perfect square since it matches $(x + 5)^2$.
$(x+5)^2$. The trinomial $x^2 + 10x + 25$ is a perfect square since it matches $(x + 5)^2$.
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State the identity for factoring a difference of squares.
State the identity for factoring a difference of squares.
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$a^2-b^2=(a-b)(a+b)$. The difference of squares identity factors $a^2 - b^2$ into $(a - b)(a + b)$.
$a^2-b^2=(a-b)(a+b)$. The difference of squares identity factors $a^2 - b^2$ into $(a - b)(a + b)$.
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What is the factored form of $x^2 - 9$ as a difference of squares?
What is the factored form of $x^2 - 9$ as a difference of squares?
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$(x-3)(x+3)$. Recognize $x^2 - 9$ as a difference of squares, where $x^2 - 3^2 = (x - 3)(x + 3)$.
$(x-3)(x+3)$. Recognize $x^2 - 9$ as a difference of squares, where $x^2 - 3^2 = (x - 3)(x + 3)$.
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Identify the factored form of $8x^2 - 12x$ using the GCF.
Identify the factored form of $8x^2 - 12x$ using the GCF.
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$4x(2x-3)$. Factor out the GCF of $4x$ from both terms, leaving $2x - 3$ inside the parentheses.
$4x(2x-3)$. Factor out the GCF of $4x$ from both terms, leaving $2x - 3$ inside the parentheses.
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What is the greatest common factor (GCF) of $12x^3y^2$ and $18x^2y^5$?
What is the greatest common factor (GCF) of $12x^3y^2$ and $18x^2y^5$?
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$6x^2y^2$. 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.
$6x^2y^2$. 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.
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What is the factored form of $ax+ay+bx+by$ by factoring by grouping?
What is the factored form of $ax+ay+bx+by$ by factoring by grouping?
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$(a+b)(x+y)$. Group terms as $(ax + ay) + (bx + by) = a(x + y) + b(x + y)$, then factor out the common binomial.
$(a+b)(x+y)$. Group terms as $(ax + ay) + (bx + by) = a(x + y) + b(x + y)$, then factor out the common binomial.
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Identify the factored form of $2x^2 - 18$ as completely as possible.
Identify the factored form of $2x^2 - 18$ as completely as possible.
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$2(x-3)(x+3)$. First factor out the GCF of 2, then factor the remaining difference of squares $x^2 - 9$.
$2(x-3)(x+3)$. First factor out the GCF of 2, then factor the remaining difference of squares $x^2 - 9$.
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Identify the factored form of $9x^2 - 12x + 4$ as a perfect square.
Identify the factored form of $9x^2 - 12x + 4$ as a perfect square.
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$(3x-2)^2$. The trinomial $9x^2 - 12x + 4$ matches the perfect square form $(3x - 2)^2$.
$(3x-2)^2$. The trinomial $9x^2 - 12x + 4$ matches the perfect square form $(3x - 2)^2$.
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State the identity for factoring a perfect square trinomial $a^2-2ab+b^2$.
State the identity for factoring a perfect square trinomial $a^2-2ab+b^2$.
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$a^2-2ab+b^2=(a-b)^2$. The perfect square trinomial identity factors $a^2 - 2ab + b^2$ as $(a - b)^2$.
$a^2-2ab+b^2=(a-b)^2$. The perfect square trinomial identity factors $a^2 - 2ab + b^2$ as $(a - b)^2$.
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What is the factored form of $x^2 - 16x + 64$ as a perfect square trinomial?
What is the factored form of $x^2 - 16x + 64$ as a perfect square trinomial?
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$(x-8)^2$. The trinomial $x^2 - 16x + 64$ is a perfect square since it matches $(x - 8)^2$.
$(x-8)^2$. The trinomial $x^2 - 16x + 64$ is a perfect square since it matches $(x - 8)^2$.
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Identify the factored form of $5x^2 - 20x$ using the GCF.
Identify the factored form of $5x^2 - 20x$ using the GCF.
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$5x(x-4)$. Factor out the GCF of $5x$ from both terms, leaving $x - 4$ inside the parentheses.
$5x(x-4)$. Factor out the GCF of $5x$ from both terms, leaving $x - 4$ inside the parentheses.
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What is the factored form of $x^2 + 6x - 16$ over the integers?
What is the factored form of $x^2 + 6x - 16$ over the integers?
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$(x+8)(x-2)$. Find two integers that multiply to -16 and add to 6, yielding factors $(x + 8)$ and $(x - 2)$.
$(x+8)(x-2)$. Find two integers that multiply to -16 and add to 6, yielding factors $(x + 8)$ and $(x - 2)$.
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Identify the factored form of $6x^2 - 54$ by factoring out the GCF first.
Identify the factored form of $6x^2 - 54$ by factoring out the GCF first.
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$6(x-3)(x+3)$. First factor out the GCF of 6, then factor the remaining difference of squares $x^2 - 9$.
$6(x-3)(x+3)$. First factor out the GCF of 6, then factor the remaining difference of squares $x^2 - 9$.
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State the identity for factoring a sum of cubes.
State the identity for factoring a sum of cubes.
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$a^3+b^3=(a+b)(a^2-ab+b^2)$. The sum of cubes identity factors $a^3 + b^3$ into $(a + b)(a^2 - ab + b^2)$.
$a^3+b^3=(a+b)(a^2-ab+b^2)$. The sum of cubes identity factors $a^3 + b^3$ into $(a + b)(a^2 - ab + b^2)$.
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State the identity for factoring a difference of cubes.
State the identity for factoring a difference of cubes.
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$a^3-b^3=(a-b)(a^2+ab+b^2)$. The difference of cubes identity factors $a^3 - b^3$ into $(a - b)(a^2 + ab + b^2)$.
$a^3-b^3=(a-b)(a^2+ab+b^2)$. The difference of cubes identity factors $a^3 - b^3$ into $(a - b)(a^2 + ab + b^2)$.
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Identify the factored form of $4x^2 - 25$.
Identify the factored form of $4x^2 - 25$.
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$(2x-5)(2x+5)$. Recognize $4x^2 - 25$ as a difference of squares, $(2x)^2 - 5^2 = (2x - 5)(2x + 5)$.
$(2x-5)(2x+5)$. Recognize $4x^2 - 25$ as a difference of squares, $(2x)^2 - 5^2 = (2x - 5)(2x + 5)$.
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What is the factored form of $3x^2 - 11x - 4$?
What is the factored form of $3x^2 - 11x - 4$?
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$(3x+1)(x-4)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(3x + 1)(x - 4)$.
$(3x+1)(x-4)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(3x + 1)(x - 4)$.
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What is the factored form of $2x^2 + 7x + 3$?
What is the factored form of $2x^2 + 7x + 3$?
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$(2x+1)(x+3)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(2x + 1)(x + 3)$.
$(2x+1)(x+3)$. Factor by finding integers where the product of leading coefficients and constants gives the quadratic, matching $(2x + 1)(x + 3)$.
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