Question

unit 7 review assignment

1. $12x^2 - 40x - 32$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(12x^2\), \(-40x\), and \(-32\). The GCF of 12, 40, and 32 is 4. So we factor out 4:
\(12x^2 - 40x - 32 = 4(3x^2 - 10x - 8)\)

Step2: Factor the quadratic

Now, factor the quadratic \(3x^2 - 10x - 8\). We need two numbers that multiply to \(3 \times (-8) = -24\) and add up to \(-10\). The numbers are \(-12\) and \(2\).
Rewrite the middle term using these numbers:
\(3x^2 - 12x + 2x - 8\)
Group the terms:
\((3x^2 - 12x) + (2x - 8)\)
Factor out the GCF from each group:
\(3x(x - 4) + 2(x - 4)\)
Now, factor out \((x - 4)\):
\((3x + 2)(x - 4)\)

Step3: Combine the factors

Putting it all together, the factored form of the original expression is:
\(4(3x + 2)(x - 4)\)

Answer:

\(4(3x + 2)(x - 4)\)