What is the remainder r when the polynomial p(x) is divided by (x+1)? p(x)=5x^4+6x^3+x^2+2x+2 r= is (x+1) a factor of p(x)? yes or no

R = 0 and (x + 1) is a factor of p(x)

Step-by-step explanation:

Using the Remainder theorem

given p(x) is divided by a factor (x + h)

Then the remainder R is p(- h)

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

factor (x + 1 ) ⇒ h = - 1

p(- 1) = 5 + 6(- 1)³ + (- 1)² + 2(- 1) + 2

        = 5 - 6 + 1 - 2 + 2 = 0 → R = 0

Hence x = - 1 is a root and (x + 1) is a factor