Question

For what value of k,x- 3 is a factor of p(x)=xcube-6xsquare+kx-6​

Answer 1

$p(x) = {x}^{3} - 6 {x}^{2} + kx - 6 \\ \\ given \\ \\ x - 3 \: is \: a \: factor \: of \: p(x) \\ \\ = > p(3) = 0 \\ \\ {3}^{3} - 6(3) {}^{2} + 3k - 6 = 0 \\ \\ k = 11$

hope it helps.

Answer 2

x^3-6x^2+kx-6

(3)^3-6(3)^2+k(3)-6=0

27-54+3k-6=0

-33+3k=0

3k=33

k=11