Question

or what value of k, is the polynomial p(x) = 2x3 – kx2 + 3x + 30 exactly divisible by (x+2)?

Answer 1

Hola

Here is your answer Friend ☺️

Question -
$p(x) = 2 x^{3} - k {}^{2} + 3x + 30$
q(x) = x + 2

x + 2 = 0

therefore x = -2

substitute x = -2 in p(x)

=
$p(x) = 2( - 2)^{3} - {k}^{2} + 3( - 2) + 30$

Therefore, p(x) = 2(-8) - k^2 -6 + 30

-16 -k^2 -6 +30

-22+30-k^2

8 - k^2

Therefore after solving this we get

$8 - {k}^{2}$
As it's written that the polynomial is completely divisible

so it means the remainder is 0.

thus,

$8 - {k}^{2} = 0 \\ {k}^{2} = 8 \\ k = \sqrt{8}$

Hope it helps !