Use the Factor Theorem to determine whether the binomial x + 1 is a factor of the polynomial function ƒ(x) = 2x3 – 9x2 + 13x – 6.

Question

No, because ƒ(c) = –4

Yes

No, because ƒ(c) = 14

No, because ƒ(c) = –30

Answer 1

ƒ(x) = 2x3 – 9x² + 13x – 6.  Is this (evenly) divisible by (x+1).  This division can be accomplished by using c = -1 in the "slot" on top line, at the left, for Synthetic Division.

 

Equivalently, if f(-1) = 0, then (x+1) is indeed a factor of f(x).

 

Direct substitution gives f(-1) = -2 -9 -13 -6 which is obviously not zero. Therefore the answer is NO, (x+1) is not a factor.

 

But since f(1) = 0, we see that (x-1) is a factor of f(x).