# Polynomial Division

• Aug 26th 2008, 05:40 AM
magentarita
Polynomial Division
I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

-4x^2 - 3x - 3 remainder -7

How can this be?

Can you show me step by step why the above answer is correct?
• Aug 26th 2008, 05:58 AM
Moo
Hello,
Quote:

Originally Posted by magentarita
I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

-4x^2 - 3x - 3 remainder -7

How can this be?

Can you show me step by step why the above answer is correct?

My method may not be like yours, but I can't manage to change it ~~

$\displaystyle -4x^3+x^2-4$ and x-1.

First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x.
$\displaystyle -4x^3={\color{green}-4x^2}(x)$.

So I'll write :
$\displaystyle -4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4$

And so on... :

$\displaystyle -4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4$

$\displaystyle (x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4$$\displaystyle =\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}} If you want to know where your mistake(s) is/are, just show your work ^^ • Aug 26th 2008, 08:52 PM magentarita Perfect! Quote: Originally Posted by Moo Hello, My method may not be like yours, but I can't manage to change it ~~ \displaystyle -4x^3+x^2-4 and x-1. First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x. \displaystyle -4x^3={\color{green}-4x^2}(x). So I'll write : \displaystyle -4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4 And so on... : \displaystyle -4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4 \displaystyle (x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4$$\displaystyle =\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}}$

If you want to know where your mistake(s) is/are, just show your work ^^

Perfectly done!