Question

let p be a polynomial function where p(x)=x4- dx3 + 8x2 - 10x + 4 if (x-2) is a factor of the polynomial, what is the value of d?

Answer 1

d = 4

Explanation:

If (x -2) is a factor of polynomial p(x), then the remainder will be zero.

⇒ p(2) = 0

`\sf \bf 2^4-d*2^3 + 8*2^2 -10*2 + 4 = 0\\\\`

16 - 8d + 8*4 - 20 + 4 = 0

16 - 8d + 32 - 20 + 4 = 0

-8d + 32 = 0

-8d = - 32

d = -32/(-8)

`\boxed{d = 4}`