Find K if x + 1 is a factor of P(x) = Kx^2-x+2

Question

asked Jul 4, 2022 125k views

1 Answer

MyLifeasdog · Answer 1 · 2022-07-08T13:33:00+0000

Answer:

K=-3

Explanation:

According to the Factor Theorem, a binomial (x - a) is a factor of a polynomial P(x) if and only if P(a) = 0.

We have the polynomial:

P(x)=Kx^2-x+2

And we want to find the value of K such that (x + 1) is a factor.

We can rewrite our factor as (x - (-1)). Thus, a = -1.

Then in orer for (x + 1) to be a factor, P(-1) must equal 0. Hence:

P(-1)=K(-1)^2-(-1)+2=0

Simplify:

K+1+2=0

Solve for K. Hence:

K=-3