Question

If x+p is a factor of p(x) = x5 -p2 x3 +2x+p+1 find the value of p

Answer 1

p = 1

Explanation:

Polynomial:

If (x + p) is a factor of p(x), then p(-p) =0

p(x) = x⁵ - p²x³ + 2x+ p + 1

x + p = 0

x = -p

p(-p) = 0

(-p)⁵ - p²*(-p)³ + 2*(-p) ++ p + 1 = 0

-p⁵ + p⁵ - 2p + p + 1 = 0

-p + 1 = 0

-p = -1

p = -1/-1

`\sf \boxed{\bf p = 1}`