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A-SSE.2 Warmup M3-016-A03-V01

Use expression structure to find useful rewrites.

Factor an expression by treating a repeated polynomial as one variable

Problem

Use the repeated sub-expression \(x^2\) to factor \(x^4~-~5x^2~+~4\) as a quadratic in form.

Grouping map highlighting every occurrence of x², mapping the complete unit to u, and showing u² − 5u + 4 without the factorization. Open full size
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What this problem is really about

An expression can be quadratic in a repeated power even when it is not written as an ordinary quadratic in x. Name the lower repeated power as one unit, so its square becomes the new variable squared. Factor that simpler quadratic first, then replace every occurrence of the temporary variable with the complete original unit.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-SSE.2
Category
Algebra
Domain
Seeing Structure in Expressions
Objective
Use expression structure to find useful rewrites.
Problem type
Factor an expression by treating a repeated polynomial as one variable