Question

If the polynomial p(x)=x 3 -kx 2 +3x+2 is exactly divisible by (x+1) then the value of k is

Answer 1

QUESTION:

If the polynomial p(x)=x 3 -kx 2 +3x+2 is exactly divisible by (x+1) then the value of k is.

ANSWER :

GIVEN:

The polynomial p(x) is exactly divisible by x+1.

so,

$x + 1 = 0 \\ x = - 1$

putting the value of x in given polynomial.

$p(x) = {x}^{3} - k {x}^{2} + 3x + 2 \\ p( - 1) = { - 1}^{3} - k( { - 1})^{2} + 3( - 1) + 2 = 0 \\ - 1 - k - 3 + 2 = 0 \\ - 1 - 3 + 2 - k = 0 \\ - 4 + 2 - k = 0 \\ - k = 2 \\ k = - 2$

FINAL ANSWER :

$k = - 2$

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