Question

find M if 2x-1 is a factor of 8x⁴+4x³-16x²+10x+m

Answer 1

x=1/2
putting the value of x in equation
8×1/2×2×2×2+4×1/2×2×2-16×1/2×2+10×1/2+m=0
on solving the equation
m=-2
hope it will help you

Answer 2

If $2x-1$ is a factor of $p(x)=8x^4+4x^3-16x^2+10x+m$ then by factor theorum,
$p(\frac{1}{2})=0\\ \Rightarrow \frac{8}{2^4}-\frac{4}{2^3}-\frac{16}{2^2}+\frac{10}{2}+m=0\\ \Rightarrow \frac{1}{2}+\frac{1}{2}-4+5+m=0\\ \Rightarrow m=-2$