Question

What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

Answer 1

Here you have two polynomials:

1. The dividend -
`f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3`

2. The divisor -
`g(x)=x^2 - 2x + 1`.

Since divisor is perfect square
`g(x)=x^2 - 2x + 1=(x-1)^2`, you should check what is the quotient after division f(x) by (x-1):

`f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3=(x-1)(2x^3-x^2-4x+3)=(x-1)(x-1)(2x^2+x-3)=(x-1)^2(2x^2+x-3)=g(x)(2x^2+x-3).`

Then the quotient is
`2x^2+x-3`.

Answer 2

Quotient:
`2x^2+x-3`

Please see the attachment.

Explanation:

Given:
`(2x^4-3x^3-3x^2+7x-3)/ (x^2-2x+1)`

We are given rational expression and need to find quotient.

Using long division method to find the quotient.

First we get rid of
`2x^4` by
`x^2`

`x^2-2x+1` )
`2x^4-3x^3-3x^2+7x-3` (
`2x^2+x-3`

`-2x^4+4x^3-2x^2`

`x^3-5x^2+7x`

`-x^3+2x^2-x`

`-3x^2+6x-3`

`3x^2-6x+3`

`0`

Hence, The quotient of division is
`2x^2+x-3`