Question

question 8 of 10
multiply the polynomials.
(x + 2)(2x² + 9x + 8)

a. 2x³ + 13x² - 26x + 16
b. 16x³ + 72x² + 46x - 16
c. 2x³ + 13x² + 26x + 16
d. 2x³ + 17x² + 22x + 16

Explanation:

Step1: Apply distributive property

Multiply \(x\) by each term in \(2x^2 + 9x + 8\) and \(2\) by each term in \(2x^2 + 9x + 8\):
\(x(2x^2 + 9x + 8) + 2(2x^2 + 9x + 8)\)
\(= 2x^3 + 9x^2 + 8x + 4x^2 + 18x + 16\)

Step2: Combine like terms

Combine \(9x^2\) and \(4x^2\), \(8x\) and \(18x\):
\(2x^3 + (9x^2 + 4x^2) + (8x + 18x) + 16\)
\(= 2x^3 + 13x^2 + 26x + 16\)

Answer:

C. \(2x^3 + 13x^2 + 26x + 16\)