Question

Use the remainder theorem and the factor theorem to determine whether (b + 4) is a factor of (b3 + 3b2 − b + 12).

A. The remainder is 0 and, therefore, (b + 4) isn't a factor of (b3 + 3b2 − b + 12).

B. The remainder is 0 and, therefore, (b + 4) is a factor of (b3 + 3b2 − b + 12).

C. The remainder isn't 0 and, therefore, (b + 4) isn't a factor of (b3 + 3b2 − b + 12).

D. The remainder isn't 0 and, therefore, (b + 4) is a factor of (b3 + 3b2 − b + 12).

Answer 1

b.........................

Answer 2

If (b+4) is a factor of f(b), then f(-4)=0.

Since f(-4)=0, the remainder is zero, and thus (b+4) is a factor of f(b).