Question

factor completely. $5x^{3}-10x^{2}+8x - 16$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(5x^3 - 10x^2) + (8x - 16)$

Step2: Factor out the GCF from each group

For the first group, the GCF of $5x^3$ and $-10x^2$ is $5x^2$: $5x^2(x - 2)$
For the second group, the GCF of $8x$ and $-16$ is $8$: $8(x - 2)$
Now we have: $5x^2(x - 2) + 8(x - 2)$

Step3: Factor out the common binomial factor

The common binomial factor is $(x - 2)$, so we factor that out: $(x - 2)(5x^2 + 8)$

Answer:

$(x - 2)(5x^2 + 8)$