Question

select the correct answer. what is the simplest form of this expression? (x - 3)(x^2 + 4x + 5) a. x^3 + 7x^2 + 7x + 15 b. x^3 + x^2 + 17x + 15 c. x^3 + x^2 - 7x - 15 d. x^3 - 7x^2 - 17x - 15

Explanation:

Step1: Use distributive property

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

Step2: Distribute $x$ and $- 3$

$x(x^{2}+4x + 5)=x^{3}+4x^{2}+5x$ and $-3(x^{2}+4x + 5)=-3x^{2}-12x - 15$

Step3: Combine like - terms

$(x^{3}+4x^{2}+5x)+(-3x^{2}-12x - 15)=x^{3}+(4x^{2}-3x^{2})+(5x-12x)-15=x^{3}+x^{2}-7x - 15$

Answer:

C. $x^{3}+x^{2}-7x - 15$