Question

LOTS OF POINTS!!!

Question:

Find the quotient.

1. (x4 + x3 + 3x2 + 3x) ÷ (x2 + x)

2. (x4 + 4x3 − 5x2 − 20x) ÷ (x2 + 4x)

Answer 1

1.
`x^(2) +3`

2.
`x^(2) -5`

Explanation:

1. I'm assuming the equation is
`(x^(4) + x^(3) +3x^(2) + 3x)` ÷
`(x^(2) +x)`

-We need to completely factor the original equation

`(x(1+x)(x^(2)+3))/(x(x+1))`

-When you divide, you're left with:
`x^(2) +3`

2. Equation:
`(x^(4) +4x^(3) -5x^(2) -20x)` ÷
`(x^(2) +4x)`

-Factor completely

`(x(4+x)(x^(2)-5))/(x(x+4))`

-Divide; final answer is:
`x^(2) -5`

Just a tip... use symbolab as well to help you with these sort of problems. It'll help you learn how to factor properly step by step, helping understand the objective here.

Answer 2

1. x^2 +3

2. x^2 -5

Explanation:

Look at my work. I'm not 100% on the second one, but here's what I got