if 2x+k is a factor of the polynomial 8x cube+4kx square +3x+k-1, then find the value of k
Answers
The final answer is -2.
Step-by-step explanation:
\ Given \ value:\\\\\ factor = (2x+k)\\\\\ expression = 8x^3+4kx^2+3x+k-1 \\\\Find: \\\\k= ?\\\\ \ Solution:\\\\\ if \ (2x+k) =0\\\\2x= -k \\\\x= \frac{-k}{2} \\\\\ put \ the \ value \ of \ x\ in \ given \ expression.\\\\\ epression: \\\\ \ 8x^3+4kx^2+3x+k-1 = 0\\\\\rightarrow \ 8(\frac{-k}{2}^3)+4k(\frac{-k}{2})^2+3(\frac{-k}{2} )+k-1 = 0\\\\\rightarrow \ 8\times \frac{-k^3}{8}+4k\times \frac{k^2}{4}+3\times \frac{-k}{2} +k-1 = 0\\\\
\rightarrow \ -k^3+k\times k^2-\frac{3k}{2} +k-1 = 0\\\\\rightarrow \ -k^3+k^3-\frac{3k}{2} +k-1 = 0\\\\\rightarrow \ \frac{-3k}{2} +k-1 = 0\\\\\rightarrow \ \frac{-3k+2k-2}{2} = 0\\\\\rightarrow \ \frac{-k-2}{2} = 0\\\\\rightarrow \ -k-2= 0\\\\\rightarrow \ -k= 2\\\\\rightarrow \ k= - 2\\\\.