Quadratic factoring patterns (ACT/SAT). Game on.

Quadratic factoring patterns (ACT/SAT) is a grade 9 math skill aligned to Common Core standard HSA.SSE.A.2: use the structure of an expression to identify ways to rewrite it. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 quadratic factoring patterns (act/sat) problems our math games drill.

CCSS HSA.SSE.A.210 questions in the bank
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Warm-upeasy

Which expression is equivalent to x2−100?x^{2} - 100\textsf{?}

x2−100=x2−102=(x−10)(x+10).x^{2} - 100 = x^{2} - 10^{2} = (x - 10)(x + 10)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x2+10x+25?x^{2} + 10x + 25\textsf{?}

Half of 1010 is 55 and 52=25,5^{2} = 25\textsf{,} so x2+10x+25=(x+5)2.x^{2} + 10x + 25 = (x + 5)^{2}\textsf{.}

Mid-gameeasy

Which expression is equivalent to 49−x2?49 - x^{2}\textsf{?}

49−x2=72−x2=(7−x)(7+x).49 - x^{2} = 7^{2} - x^{2} = (7 - x)(7 + x)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x2+12x+36?x^{2} + 12x + 36\textsf{?}

Half of 1212 is 66 and 62=36,6^{2} = 36\textsf{,} so x2+12x+36=(x+6)2.x^{2} + 12x + 36 = (x + 6)^{2}\textsf{.}

Mid-gameeasy

Which expression is equivalent to x2−14x+49?x^{2} - 14x + 49\textsf{?}

Half of 1414 is 77 and 72=49,7^{2} = 49\textsf{,} so x2−14x+49=(x−7)2.x^{2} - 14x + 49 = (x - 7)^{2}\textsf{.}

Mid-gameeasy

Which expression is equivalent to x2−121?x^{2} - 121\textsf{?}

x2−121=x2−112=(x−11)(x+11).x^{2} - 121 = x^{2} - 11^{2} = (x - 11)(x + 11)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x2+16x+64?x^{2} + 16x + 64\textsf{?}

Half of 1616 is 88 and 82=64,8^{2} = 64\textsf{,} so x2+16x+64=(x+8)2.x^{2} + 16x + 64 = (x + 8)^{2}\textsf{.}

Buzzer beatereasy

Which expression is equivalent to 4x2−9?4x^{2} - 9\textsf{?}

4x2−9=(2x)2−32=(2x−3)(2x+3).4x^{2} - 9 = (2x)^{2} - 3^{2} = (2x - 3)(2x + 3)\textsf{.}

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover quadratic factoring patterns (act/sat):
SATPSAT 8/9SBACNY State MathMCAP
Reporting domains for this skill
SAT All grades: Advanced MathACT All grades: Preparing for Higher MathSTAAR Algebra I: Number and Algebraic MethodsSTAAR Algebra I: Quadratic Functions and EquationsMAP Growth Math 6+: Operations and Algebraic ThinkingSBAC High School: Concepts and Procedures
More Grade 9 skills
Quadratic expression values from equationsQuadratic function word problems (ACT)Quadratic distinct real solutions countQuadratic minimum from vertex formProduct systems that compare numbersQuadratic minimum x-valuePolynomial expression multiplication (SAT)Quadratic missing coefficient from roots (ACT)All Grade 9 practice →

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