Question

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: Distribute $x$ to the trinomial

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

Step2: Distribute $-3$ to the trinomial

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

Step3: Combine the two results

$(x^3 + 4x^2 + 5x) + (-3x^2 - 12x - 15)$

Step4: Combine like terms

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

Answer:

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