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

1 Answer
Mar 25, 2017

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)#