Question

describe the steps you would use to factor $2x^3 + 5x^2 - 8x - 20$ completely. then state the factored form.

Explanation:

Step1: Group terms into pairs

Group the first two and last two terms:
$(2x^3 + 5x^2) + (-8x - 20)$

Step2: Factor out GCF from each pair

Factor $x^2$ from first pair, $-4$ from second pair:
$x^2(2x + 5) - 4(2x + 5)$

Step3: Factor out common binomial

Factor out $(2x + 5)$ from both terms:
$(2x + 5)(x^2 - 4)$

Step4: Factor difference of squares

Rewrite $x^2 - 4$ as $x^2 - 2^2$ and factor:
$(2x + 5)(x - 2)(x + 2)$

Answer:

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