Question

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

Answer 1

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

Explanation:

At first rewrite the expression into this form:
`(x^3-2x^2-4x+5)`:`(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)`:`(x-3) =x^2` , because `x^3/x=x^2`
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`

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

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

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

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