Question

Find k if (x-1) is factor of 2x³+9x²+x+k​

Answer 1

$\huge\boxed{\fcolorbox{black}{pink}{Solution}}$

k = -12

$\small{\underline{\sf{\pink{step \: by \: step \: solution}}}}$

$f(x) = {2x}^{3} + {9x}^{2} + \times + k$

$If (x-1) is \: a \: factor$

$then , x - 1 = 0 \\ x = 1$

$f(1) = 0$

$f(1) = 2. {1}^{3} + 9. {1}^{2} + 1 + k$

$2 + 9 + 1 +k = 0$

$12 + k = 0$

$k \: = \: - 12$