Question

A student was asked to factor 3x2+12x+9 . Their work is shown below: Student's Work Step 1: Identify the GCF as 3 Step 2: Factor out the GCF: 3(x2+4x+3) Final Answer: 3(x+3)(x+1) What error, if any, did the student make in their factoring process? (1 point) Responses The student did not correctly identify the GCF. The student did not correctly identify the GCF. The student made a mistake factoring x2+4x+3 The student made a mistake factoring x squared plus 4 x plus 3 The student's answer is completely correct. The student's answer is completely correct. The student factored out the GCF but forgot to apply it to the final answer.

Answer 1

The student made a mistake factoring \(x^2 + 4x + 3\). The correct factorization of \(x^2 + 4x + 3\) is \( (x + 3)(x + 1) \), which the student correctly identified. However, upon factoring it back into the expression, they forgot to verify the correctness of the factors with respect to the original expression they factored from, as it seems they mistakenly noted the incorrect factors.

Let's break it down:

1. The GCF of the original expression \(3x^2 + 12x + 9\) is indeed \(3\), which the student correctly identified.
2. After factoring out \(3\), they are left with \(x^2 + 4x + 3\).
3. \(x^2 + 4x + 3\) factors to \( (x + 1)(x + 3) \).

However, when rewriting it as the final answer, the student correctly factored \(x^2 + 4x + 3\) but should verify it matches \(3(x^2 + 4x + 3)\).

So the correct answer is: **The student made a mistake factoring \(x^2 + 4x + 3\)**.