SOLUTION: Find the quotient and remainder when P(x) is divided by D(x). P(x)= x^4 + x^3 +2x^2 +x+1 ; D(x)= x^2-2x+1

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the quotient and remainder when P(x) is divided by D(x). P(x)= x^4 + x^3 +2x^2 +x+1 ; D(x)= x^2-2x+1      Log On


   

Question 983606: Find the quotient and remainder when P(x) is divided by D(x).
P(x)= x^4 + x^3 +2x^2 +x+1 ; D(x)= x^2-2x+1
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-2x+1 ;; divide into x^4 + x^3 +2x^2 +x+1
First term is x^2, and you have x^4-3x^3+x^2 underneath.
subtract, and you have 3x^3+x^2+x
Second term is 3x, and you have 3x^3-6x^2+3x underneath.
Subtract, and you have 7x^2-2x+1
Third term is 7, and you have 7x^2-14x+7
Subtract, and you have 12x-6 remainder
if you multiply (x^2-2x+1)and (x^2+3x+7), you obtain
x^4+x^3+2x^2-11x+7. If you add the two, you get the original polynomial divisor.
quotient is x^2+3x+7; remainder 12x-6