Question

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.

2x2 – 9x

x2 + 6x – 24

x2 – 2x – 9

–4x2 + 8x + 36

Answer 1

Base area = volume ÷ height = (x^3 + 2x^2 − 17x − 36)/(x + 4).

Synthetic division by −4 (root of x + 4):

Coefficients: 1, 2, −17, −36
Bring down 1
Multiply −4·1 = −4; add to 2 → −2
Multiply −4·(−2) = 8; add to −17 → −9
Multiply −4·(−9) = 36; add to −36 → 0

Quotient: x^2 − 2x − 9.

Answer: x^2 − 2x − 9.