Here you have two polynomials:
1. The dividend - [tex] f(x)=2x^4 - 3x^3 - 3x^2 + 7x - 3 [/tex]
2. The divisor - [tex] g(x)=x^2 - 2x + 1 [/tex].
Since divisor is perfect square [tex] g(x)=x^2 - 2x + 1=(x-1)^2 [/tex], you should check what is the quotient after division f(x) by (x-1):
[tex] 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). [/tex]
Then the quotient is [tex] 2x^2+x-3 [/tex].
Answer:
Quotient: [tex]2x^2+x-3[/tex]
Please see the attachment.
Step-by-step explanation:
Given: [tex](2x^4-3x^3-3x^2+7x-3)\div (x^2-2x+1)[/tex]
We are given rational expression and need to find quotient.
Using long division method to find the quotient.
First we get rid of [tex]2x^4[/tex] by [tex]x^2[/tex]
[tex]x^2-2x+1[/tex] ) [tex]2x^4-3x^3-3x^2+7x-3[/tex] ( [tex]2x^2+x-3[/tex]
[tex] -2x^4+4x^3-2x^2[/tex]
[tex]x^3-5x^2+7x[/tex]
[tex]-x^3+2x^2-x[/tex]
[tex]-3x^2+6x-3[/tex]
[tex] 3x^2-6x+3[/tex]
[tex]0[/tex]
Hence, The quotient of division is [tex]2x^2+x-3[/tex]
