How do you divide (x^3 - 2x^2 - 4x + 5) /( x - 3)x3−2x2−4x+5x−3?

1 Answer
Juzun
Mar 25, 2017

The solution of the expression is: x^2+x-1+2/(x-3)x2+x−1+2x−3.

Explanation:

At first rewrite the expression into this form:
(x^3-2x^2-4x+5)(x3−2x2−4x+5):(x-3) =(x−3)=

We will divide the term of the first polynomial by the first term in the second polynomial:
(x^3-2x^2-4x+5)(x3−2x2−4x+5):(x-3) =x^2(x−3)=x2 , because x^3/x=x^2x3x=x2
Now we will multiply the second polynomial by our first term of the result and deduct it from the first polynomial:
(x^3-2x^2-4x+5)-x^2*(x-3)=x^2-4x+5(x3−2x2−4x+5)−x2⋅(x−3)=x2−4x+5

We have a new polynomial x^2-4x+5x2−4x+5 and we have to do the same as in the first step:
(x^2-4x+5)(x2−4x+5):(x-3)=x(x−3)=x
Now multiply and deduct:
(x^2-4x+5)-(x-3)*x=-x+5(x2−4x+5)−(x−3)⋅x=−x+5

(-x+5)(−x+5):(x-3)=-1(x−3)=−1
(-x+5)-(x-3)*(-1)=2(−x+5)−(x−3)⋅(−1)=2

The last term of the polynomial will be divided by the entire second polynomial:
2/(x-3)2x−3

The final result is the sum of each result:
x^2+x-1+2/(x-3)x2+x−1+2x−3

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