Posted by Sarah on .
Directions: Find the quotient and the remainder when the first polynomial is divided by the second.
#9. 3x^4 – 2x^3 + 5x^2 + x + 1;x^2 + 2x

Discrete Math 
MathMate,
Do exactly as you would do in a long division of numbers:
3x^4 – 2x^3 + 5x^2 + x + 1;x^2 + 2x
I will do it below, but the coefficients will not be lined up because I do not know how to insert spaces that don't get merged at this forum.
Divide x^2+2x into
3x^4 – 2x^3 + 5x^2 + x + 1
First divide 3x^4 by x^2 to get 3x^2.
Then multiply (x^2+2x) by 3x^2 to get
3x^4+6x^3
Subtract 3x^4+6x^3 from 3x^4 – 2x^3 + 5x^2 + x + 1 to get
– 8x^3 + 5x^2 + x + 1
Repeat the same as above:
Divide 8x^3 by x^2 to get 8x
Multiply x^2+2x by 8x to get 8x^3 16x^2.
Subtract 8x^3 16x^2 from – 8x^3 + 5x^2 + x + 1 to get 21x^2 +x + 1.
The same process will repeat itself to get the final answer by collecting all the above quotient terms:
3x^28x+21 with a remainder of 41x+1