Thread: Theorems

1)Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3 +3b^2 - b+12)

A. The remainder is 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
B. The remainder is 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)
C. The remainder isn't 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
D. The remainder isn't 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)

2) Use the remainder theorem to determine the remainder the remainder when 3t^2 +5t -7 is divided by t-5

3)Use the remainder theorem and the factor theorem to determine whether (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)

A. The remainder is 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
B. The remainder is 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)
C. The remainder isn't 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
D. The remainder isn't 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)

Hello, pyrogurl6989!

I will assume you know the Remainder Theorem and the Factor Theorem.

1) Use the remainder theorem and the factor theorem to determine
whether is a factor of

Since

. . then: .(A) The remainder is 0, and therefore is a factor of

2) Use the remainder theorem to determine the remainder
when is divided by

Since , then the remainder is

3)Use the remainder theorem and the factor theorem to determine
whether is a factor of

Since

. . then: .(A) The remainder is 0, and therefore is a factor of