The Factor Theorem

Question

Use the Factor Theorem to determine whether x - 2 is a factor of P(x) = x⁴ - x³ + 3x - 14 .Specifically, evaluate P at the proper value, and then determine whether x - 1 is a factor.

Is x-2 a factor of P(x) or not

P(?) = ?

Answer 1

P(2) = 2^4 -2^3 +3(2) -14 = 16-8+6-14 = 0

P(2) =0 so x-2 is a factor

P(1) = 1-1+3 -14 = -11

P(1) =-11, so x-1 is Not a factor

P(a) has to equal zero, for x-a to be a factor of P(x)