Question

Louise begins factoring the polynomial, which has four terms.

Answer 1

Louise wants to factorize completely the given polynomial $4x^{3}+12x^{2}+5x+15$

Grouping first, second terms together and third, fourth terms together

= $4x^{3}+12x^{2}+5x+15$

Taking $4x^{2}$ common from first and second terms of the given expression and taking 5 common from the third and fourth terms.

=$=4x^{2}(x+3)+5(x+3)$

Taking (x+3) common from the given expression,

=$=(4x^{2}+5)(x+3)$ is the completely factored form.