Question

1. what is $(3x + 7)(5x^2 - 3x + 4)?$

a. $15x^3 + 27x^2 + 12x + 28$

b. $15x^3 + 26x^2 + 12x + 27$

c. $15x^3 + 26x^2 - 9x + 28$

d. $15x^3 + 26x^2 + 13x + 27$

Explanation:

Step1: Distribute first term

$3x(5x^2 - 3x + 4) = 15x^3 - 9x^2 + 12x$

Step2: Distribute second term

$7(5x^2 - 3x + 4) = 35x^2 - 21x + 28$

Step3: Combine like terms

$15x^3 + (-9x^2+35x^2) + (12x-21x) + 28$
$=15x^3 + 26x^2 -9x +28$

Answer:

c. $15x^{3}+26x^{2}-9x+28$