Question

If X + K is a factor of the polynomial x cube + k x square - 2 X + K + 4 find the value of k

Answer 1

Answer:

$x + k \: is \: a \: factor \: of \: given \: \\ polynomial \\ - k \: is \: zero \: of \: polynomial \\ now \: let \: us \: substitute \: x = - k \: \\ in \: {x}^{3} + k {x}^{2} -2 x + k + 4 \: we \: find \\ {( - k)}^{3} + k \times {( - k)}^{2} -2 ( - k) + 4 = 0 \\ - {k}^{3} + {k}^{3} + 2k + 4 = 0 \\ 2k + 4 = 0 \\ 2k = - 4 \\ k = - \frac{4}{2} \\ k = - 2$