Question

question
factor completely.
$16x^3 + 112x^2 - x - 7$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(16x^{3}+112x^{2})+(-x - 7)$

Step2: Factor out the GCF from each group

Factor out $16x^{2}$ from the first group and $-1$ from the second group: $16x^{2}(x + 7)-1(x + 7)$

Step3: Factor out the common binomial factor

Factor out $(x + 7)$: $(x + 7)(16x^{2}-1)$

Step4: Factor the difference of squares

Notice that $16x^{2}-1$ is a difference of squares, which factors as $(4x + 1)(4x - 1)$

Answer:

$(x + 7)(4x + 1)(4x - 1)$