P(x) = 5x4 + 2x3 − 5x2 − 2x + 1 divided by binomial: x − 1

Question

Use the Remainder Theorem to find the remainder that occurs when
P(x) = 5x4 + 2x3 − 5x2 − 2x + 1
is divided by the binomial.
x − 1

Answer 1

If a polynomial function f(x) is divided by x-c, then the remainder is f(c).

 

So, if P(x) = 5x⁴ + 2x³ - 5x² - 2x + 1 is divided by x-1, then the remainder is 

 

   P(1) = 1