Question

question
factor completely.
$8x^3 - 20x^2 - 50x + 125$
answer attempt 2 out of 2
$(4x^2 - 25)(2x - 5)$
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Explanation:

Step1: Group terms

Group the first two terms and the last two terms: $(8x^3 - 20x^2) + (-50x + 125)$

Step2: Factor out GCF from each group

Factor out $4x^2$ from the first group and $-25$ from the second group: $4x^2(2x - 5) - 25(2x - 5)$

Step3: Factor out common binomial factor

Factor out $(2x - 5)$: $(4x^2 - 25)(2x - 5)$

Step4: Factor difference of squares

Notice that $4x^2 - 25$ is a difference of squares, so factor it: $(2x - 5)(2x + 5)(2x - 5)$

Step5: Combine like factors

Combine the two $(2x - 5)$ factors: $(2x - 5)^2(2x + 5)$

Answer:

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