Grade 9 · Algebra & functions

Factoring quadratics practice

Factoring quadratics 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 30 factoring quadratics problems our math games drill.

CCSS HSA.SSE.A.230 questions in the bank

Sample questions

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Question 1easy

$x^{2} - 9 = (x - c)(x + c)$ with $c > 0$ . What is $c$ ?

Difference of squares: $x^{2} - 9 = (x - 3)(x + 3)$ , so $c = 3$ .

Question 2easy

$x^{2} + kx + 18$ factors as $(x - 3)(x - 6)$ . What is $k$ ?

Expanding, $(x - 3)(x - 6) = x^{2} - 9x + 18$ , so $k = -3 + (-6) = -9$ .

Question 3easy

$x^{2} + 5x + 6 = (x + a)(x + b)$ with $a < b$ . What is $a$ ?

Two numbers that multiply to $6$ and add to $5$ are $2$ and $3$ , so $a = 2$ and $b = 3$ .

Question 4easy

$6x^{2} + 9x = 3x(2x + c)$ . What is $c$ ?

Dividing each term by the common factor $3x$ gives $6x^{2} \div 3x = 2x$ and $9x \div 3x = 3$ , so $c = 3$ .

Question 5easy

Factor: $x^2 + 7x + 12$ .

Find two numbers that multiply to 12 and add to 7: $3$ and $4$ .

Question 6easy

Solve $x^{2} - 5x + 6 = 0$ by factoring and enter the larger solution.

$x^{2} - 5x + 6 = (x - 2)(x - 3) = 0$ , so $x = 2$ or $x = 3$ ; the larger solution is $3$ .

Question 7easy

$x^{2} - 25 = (x + d)(x - d)$ with $d > 0$ . What is $d$ ?

Difference of squares: $x^{2} - 25 = (x + 5)(x - 5)$ , so $d = 5$ .

Question 8easy

$x^{2} - 6x + c$ factors as $(x - 1)(x - 5)$ . What is $c$ ?

Expanding, $(x - 1)(x - 5) = x^{2} - 6x + 5$ , so $c = (-1)(-5) = 5$ .

Tests that cover factoring quadratics:

SAT PSAT 8/9 SBAC NY State Math MCAP

More Grade 9 skills:

Factoring patterns Inconsistent linear systems Exponential functions in context (SAT)Linear equation expressions Evaluating functions from percent change Linear equation forms Linear equation from two points (SAT)Evaluating functions at a value All Grade 9 practice →

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