How do I divide and solve the following monomial problems?

Question

1) 4x^2+2x-1 / x+3
2) 6x^2-x+6 / 2x-1
3) 2x^3-14x+2 / x+3

I need to know how to do these sample problems for a test I am having in Algebra I this week, thanks.

Answer 1

Use synthetic division, similar to long division, only with polynomials. Unfortunately, it's rather hard to describe here. I'll do the first one. The numbers below represent coefficients of polynomials.

4 -10
______
1 3 | 4 2 -1
4 12
-10-1
-10 -30
29

Put another way:
4x^2+2x-1=4x(x+3)-10x-1.
-10x-1=-10(x+3)+29.

So the quotient is 4x-10, and the remainder is 29, meaning 4x^2+2x-1=(4x-10)(x+3) + 29/(x+3).

Answer 2

1. 4 2 -1
0 -12 30
---------------------
4 -10 29
so Q=4x-10 and the remainder=29

2. 6 -1 6
0 3 1
---------------------
6 2 7

quotient=3x+1 and remainder=7

3. 2 0 -14 2
0 -6 18 -12
-----------------------------
2 -6 4 -10

quotient=2x^2-6x+4 and remainder=-10
2x^2-6x+4=2x^2-2x-4x+4=(2x-1)(x-2)

Answer 3

You can use synthetic division like the guy above me said or long division. Synthetic is easier once you learn how but you can probably teach yourself long division because it's just like normal.

Answer 4

use long division...like how you divide ..example 34531/6

Qn 1) Ans : 4x-10-(29/(x+3))

E rest...try it out