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

##### 1 Answer

#### Explanation:

Note that if

#frac{a(x)}{b(x)}=Q(x)+frac{R(x)}{b(x)}# ,

then

#a(x)=b(x)Q(x)+R(x)# .

In this case,

We are interested in finding

First, observe that the degree of the polynomial in the numerator is greater than the degree of the polynomial in the denominator.

Divide the leading term of the numerator by the leading term of the denominator to get the first term of

#frac{2x^4}{x^2}=2x^2#

Multiply the result back with

Now, subtract the result from the numerator.

So now we can say that

Now observe that the degree of the numerator is still not less than that of the denominator.

As done previously, divide the leading term of the numerator by the leading term of the denominator to get the second term of

#frac{x^2}{x^2}=1#

Multiply the result back with

Now, subtract the result from the numerator.

So now we can say that

Observe that the degree of the numerator is less than that of the denominator. We are done.