Problem preview

A-SSE.1.b Warmup M3-015-A07-V02

Interpret complex polynomial/rational expressions by treating parts as single units.

Rewrite using a repeated sub-expression as u

Problem

Let \(u~=~(x~-~3)^2\) in \((x~-~3)^4~+~2(x~-~3)^2~+~1\). Rewrite the complete expression in \(u\) and factor it.

Answer choices

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Let u=x-3. Then the expression is u⁴+2u²+1=(u²+1)².

Let u=(x-3)². Then the expression is u²+2u+1=(u+1)².

Let u=(x-3)⁴. Then the expression is u+2√u+1, with u≥0.

Let u=(x-3)². Then the expression is u⁴+2u²+1=(u+1)².

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Curriculum context

Course: Math III
Standard: A-SSE.1.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Interpret complex polynomial/rational expressions by treating parts as single units.
Problem type: Rewrite using a repeated sub-expression as u