Question

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

Answer 1

Answer:

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

Please see the attachment.

Step-by-step explanation:

Given: $(2x^4-3x^3-3x^2+7x-3)\div (x^2-2x+1)$

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 $2x^2+x-3$

Answer 2

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 $2x^2+x-3$.