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

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

0 thoughts on “Find K if x + 1 is a factor of P(x) = Kx^2-x+2”

  1. Answer:

    [tex]K=-3[/tex]

    Step-by-step explanation:

    According to the Factor Theorem, a binomial (xa) 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]

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