Question

instructions
choose the best answer. if necessary, use the paper you were given.

question
which of the following is not a factor of $4x^2 + 12x - 16$?

○ 4

○ $(x - 1)$

○ $(x - 4)$

○ $(x - 4)$

Explanation:

Step1: Factor out the greatest common factor

First, factor out the greatest common factor of the terms in \(4x^{2}+12x - 16\). The GCF of \(4x^{2}\), \(12x\), and \(- 16\) is \(4\). So we have:
\(4x^{2}+12x - 16=4(x^{2}+3x - 4)\)

Step2: Factor the quadratic expression

Now, factor the quadratic \(x^{2}+3x - 4\). We need two numbers that multiply to \(-4\) and add up to \(3\). The numbers are \(4\) and \(- 1\). So:
\(x^{2}+3x - 4=(x + 4)(x - 1)\)

Step3: Combine the factors

Putting it all together, \(4x^{2}+12x - 16 = 4(x + 4)(x - 1)\)

Now we check each option:

• \(4\) is a factor (from the first step).
• \((x - 1)\) is a factor (from the second step).
• \((x - 4)\) is not a factor, since we have \((x + 4)\) and \((x - 1)\) as the linear factors (and \(4\) as the constant factor).

Answer:

\((x - 4)\) (assuming the repeated option was a typo and the third option is \((x - 4)\))