Problem preview

A-SSE.2 Warmup M2-010-A03-V02

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

Factor a perfect-square trinomial

Problem

Factor \(x^{2}-14x+49\) as a perfect square. Use the square roots of the outer terms, determine the binomial sign from the middle term, verify \(-2ab\), and expand to check.

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Roots x and 49; middle check uses the constant directly; minus sign; factorization (x − 49)²; expansion x² − 98x + 2401.

Roots x and 14; middle check −2(x)(14) = −28x; minus sign; factorization (x − 14)²; expansion x² − 28x + 196.

Roots x and 7; middle check −2(x)(7) = −14x; minus sign; factorization (x − 7)²; expansion x² − 14x + 49.

Roots x and 7; middle check has reversed sign +14x; plus sign; factorization (x + 7)²; expansion x² + 14x + 49.

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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