what is the quotient of (2x^4-3x^3–3x^2+7x-3)/(c^2-2x+1)

To do the long division, divide each term by [tex]x^2[/tex] and then subtract the product of the result and [tex]x^2 - 2x + 1[/tex] from the remaining part of the equation.

Whatever term/value you obtain from each step of the division is a part of the quotient.

When you reach 0, you have gotten to the end of the division.

Check the steps carefully and follow them below:

Step 1:

Divide [tex]2x^4[/tex] by [tex]x^2[/tex]. You get [tex]2x^2[/tex].

Step 2

Multiply [tex]2x^2[/tex] by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3[/tex]:

[tex]2x^4 - 3x^3 - 3x^2 + 7x - 3 - (2x^4 - 4x^3 + 2x^2)[/tex] = [tex]x^3 - 5x^2 + 7x - 3[/tex]

Step 3

Divide [tex]x^3[/tex] by [tex]x^2[/tex]. You get x.

Step 4

Multiply x by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]x^3 - 5x^2 + 7x - 3[/tex]:

[tex]x^3 - 5x^2 + 7x - 3 - (x^3 - 2x^2 + x) = -3x^2 +6x - 3[/tex]

Step 5

Divide [tex]-3x^2[/tex] by [tex]x^2[/tex]. You get -3

Step 6

Multiply -3 by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]-3x^2 +6x - 3[/tex]:

[tex]-3x^2 +6x - 3 - (-3x^2 + 6x -3) = 0[/tex]

From the three divisions, we got [tex]2x^2[/tex], x and -3.

Therefore, the quotient is [tex]2x^2 + x - 3[/tex].