Question

Find the value of k , x+2 is a factor of the polynomial 2x⁴+3x³+2kx²+3+6​

Answer 1

Step-by-step explanation:

$\green{question::}$

$to \: find \: the \: value \: of \: k$

$\red{given::}$

$(x + 2) \: is \: a \: factor \: of \\ 2 {x}^{4} + 3 {x}^{3} + 2k {x}^{2} + 3x + 6 = 0$

$\black{solution::}$

$we \: can \: replace \: - 2 \: where ever \\ we \: see \: x$

$2 {( - 2)}^{4} + 3 {( - 2)}^{3} + 2( { - 2)}^{2} k + 3( - 2) + 6 = 0$

$32 + ( - 24) + 8k + ( - 6) + 6 = 0$

$8 + 8k = 0$

$8k = - 8$

$k = - 1$

$\blue{thus\:the\:value\:of\:k\:is\:-1}$

thank you!!!