Question

Determine, if possible, if (x – 8) is a factor of (x3 – 3x2 – 31x – 72). A. Only if x = 2 B. Yes C. No D. Not enough information to determine

Answer 1

The polynomial remainder theorem says when we divide polynomial f(x) by x-a we'll get remainder f(a).

$f(x)=x^3 - 3x^2 - 31x - 72$

$f(8)=8^3 - 3(8^2) - 31(8) - 72$

$f(8)=512 - 3(64) - 31(8) - 72 = 512-192-248-72 = 0$

Since f(8)=0 that means x-8 has a remainder zero when divided by f(x). In other words, it's a factor of f(x).

Answer B
 

Answer 2

I believe the answer is C