Question

question
factor completely.
$27x^3 + 45x^2 - 3x - 5$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms: $(27x^3 + 45x^2) + (-3x - 5)$

Step2: Factor out GCF from each group

Factor out $9x^2$ from the first group and $-1$ from the second group: $9x^2(3x + 5) - 1(3x + 5)$

Step3: Factor out common binomial

Factor out $(3x + 5)$: $(3x + 5)(9x^2 - 1)$

Step4: Factor difference of squares

Factor $9x^2 - 1$ as a difference of squares: $(3x + 5)(3x - 1)(3x + 1)$

Answer:

$(3x + 5)(3x - 1)(3x + 1)$