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fgiga [73]
3 years ago
14

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

Mathematics
1 answer:
wlad13 [49]3 years ago
8 0

Answer:

K=-3

Step-by-step explanation:

According to the Factor Theorem, a binomial (<em>x</em> - <em>a</em>) 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 <em>K</em> such that (<em>x</em> + 1) is a factor.

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

Then in orer for (<em>x</em> + 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 <em>K. </em>Hence:

K=-3

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