Use the Remainder Theorem to find the remainder that occurs when P(x) = 5x4 + 2x3 − 5x2 − 4x + 4 is divided by the binomial. x − 1

Question

Use the Remainder Theorem to find the remainder that occurs when P(x) = 5x⁴ + 2x³ − 5x² − 4x + 4

 is divided by the binomial.

x − 1

Answer 1

First set x-1=0

Solve for x by adding 1 to both sides so

x=1

then substitute 1 in every x in the equation

P(x) = 5x⁴ + 2x³ − 5x² − 4x + 4

P(x)= 5(1)⁴+2(1)³-5(1)²-4(1)+4

=5+2-5-4+4=2

So the Remainder is 2