Question

Given that (x - 2) is a factor of this polynomial, use the Factor Theorem to find the value of a.

P(x) = x^4 - 3x^3 + Ax^2 - 6x + 14

Answer 1

the factor theorem states that if (x-a) is a factor of P(x) the P(a) = 0 so we can write, for this polynomial:

2^(4) - 3(2)^3 + A(2)^2 - 6(2) + 14 = 0

16 - 24 + 4A - 12 + 14 = 0
4A = -16+24 + 12 - 14 = 6
A = 6/4 = 1.5