Find the value of m so that 2x – 1 be a factor of 8

let p(x) = 8x4 + 4x3−16x2 + 10x + m and g(x) = 2x – 1

Putting g(x) = 0 ⟹ 2x – 1 = 0 ⟹ x = 1/2


According to the factor theorem if g(x) is a factor of p(x) then p (1/2) = 0


p(1/2) = 8(1/2)4 + 4(1/2)3−16(1/2)2 + 10(1/2) +

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