Question

for what value of k is the polynomial 2x⁴+3x³+2kx²+3x+6 exactly divisible by x+2​

Answer 1

Answer:

k = -1

Step-by-step explanation:

$g(x) = 2 {x}^{4} + 3 {x}^{3} + {2kx}^{2} + 3x + 6$

$f(x) = x + 2$

Now:-

Zero Of Polynomial g(x) :-

=)x + 2 = 0

=)x = -2

BY REMAINDER THEORAM :-

(Please Slide for right for answet < < )

$f( - 2) = 0 \\ = )(2 \times {( - 2)}^{4} ) + (3 \times ( { - 2)}^{3} ) + (2 \times k \times {( - 2)}^{2} + (3 \times - 2) + 6 = 0 \\ = )(2 \times 16) + (3 \times - 8) + (2 \times k \times 4) - 6 + 6 = 0 \\ = )32 - 24 + 8k = 0 \\ = )8 + 8k = 0 \\ = )8k = - 8 \\ = )k = - 1$

Hope it helped