Find the value of m, so that 2x-1 be a factor of
`8x^(4)+4x^(3)-16x^(2)+10+m` .

Explanation

let `p(x) =8x^(4)+4x^(3)-16x^(2)+10x+m`
Since , 2x-1 is a factor of p (x) then put `p((1)/(2))=0`
`therefore 8((1)/(2))^(4)+4((1)/(2))^(3)-16((1)/(2))^(2)+10((1)/(2))+m=0`
`implies 8xx(1)/(16)+4xx(1)/(8) -16xx(1)/(4) +10((1)/(2))+m=0`
`implies (1)/(2) +(1)/(2)-4+5+m=0`
`implies 1+1+m=0`
`therefore m=-2`
hence , the value of m is -2.