Question

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

Answer 1

`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`