Question

factor $2x^{4}+4x^{3}-5x - 10$ completely.

Explanation:

Step1: Group terms for factoring

Group the polynomial into two pairs:
$(2x^4 + 4x^3) + (-5x - 10)$

Step2: Factor out GCF from each group

Factor the greatest common factor from each pair:
$2x^3(x + 2) - 5(x + 2)$

Step3: Factor out common binomial

Factor out the shared binomial $(x + 2)$:
$(x + 2)(2x^3 - 5)$

Answer:

$(x + 2)(2x^3 - 5)$