Find K if x + 1 is a factor of P(x) = Kx^2-x+2 July 31, 2021 by Thành Đạt Find K if x + 1 is a factor of P(x) = Kx^2-x+2

Answer: [tex]K=-3[/tex] Step-by-step 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: [tex]P(x)=Kx^2-x+2[/tex] 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: [tex]P(-1)=K(-1)^2-(-1)+2=0[/tex] Simplify: [tex]K+1+2=0[/tex] Solve for K. Hence: [tex]K=-3[/tex] Reply

Answer:[tex]K=-3[/tex]

Step-by-step 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:

[tex]P(x)=Kx^2-x+2[/tex]

And we want to find the value of

Ksuch 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:[tex]P(-1)=K(-1)^2-(-1)+2=0[/tex]

Simplify:

[tex]K+1+2=0[/tex]

Solve for

K.Hence:[tex]K=-3[/tex]