Problem preview

A-SSE.2 Warmup M2-010-A03-V04

Use expression structure to identify useful rewrites, such as difference-of-squares factoring.

Factor a perfect-square trinomial

Problem

Factor \(9x^{2}-24x+16\) as a perfect-square trinomial. Identify the roots of the square terms, use the negative middle term to set the binomial sign, verify \(-2ab\), and expand.

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Roots 3x and 4; middle check −2(3x)(4) = −24x; minus sign; factorization (3x − 4)²; expansion 9x² − 24x + 16.

Roots x and 16; middle check uses the constant directly; minus sign; factorization (x − 16)²; expansion x² − 32x + 256.

Roots 3x and 24; middle check −2(3x)(24) = −144x; minus sign; factorization (3x − 24)²; expansion 9x² − 144x + 576.

Roots 3x and 4; middle check has reversed sign +24x; plus sign; factorization (3x + 4)²; expansion 9x² + 24x + 16.

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Curriculum context

Course: Math II
Standard: A-SSE.2
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Problem type: Factor a perfect-square trinomial