Back to Rewrite expressions using structure — Problem 3 · Task Set 3

HSA.SSE.A.2 Tutor Intake — Rewriting Expressions Using Structure

This short check helps your tutor understand where to start. Answer each question on your own — no notes or calculator. If you're not sure, give your best try. The goal is to find what to work on together, not to grade you.

Grade 9·10 problems·~15 min·Common Core Math - HS Algebra·standard·hsa-sse-a-2

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Procedures

A student factors $x^4 + 7x^2 + 12$ by letting $u = x^2$ ,
rewriting as $u^2 + 7u + 12$ , and factoring it as $(u + 3)(u + 4)$ .

After substituting back, the factored form of the original expression
is $(x^2 + 3)(x^2 + 4)$ .

Evaluate the original expression at $x = 1$ to verify. What is the
value of $x^4 + 7x^2 + 12$ when $x = 1$ ?