4x^2-9

(2x^3)+(3x^2)+8x+12

Anyone know how to simplify this equation?

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- Sep 18th 2008, 10:03 AMgearshifterEquation Simplification
__4x^2-9__

(2x^3)+(3x^2)+8x+12

Anyone know how to simplify this equation? - Sep 18th 2008, 10:11 AM11rdc11
Does it look like this?

$\displaystyle \frac{4x^2-9}{2x^3} +3x^2 + 8x + 12$ - Sep 18th 2008, 10:13 AMgearshifter
__4x^2-9_______________

2x^3+3x^2+8x+12

oh sorry, the top is over everything - Sep 18th 2008, 10:20 AMMoo
Hello,

Note that $\displaystyle 4x^2-9=(2x)^2-3^2$. This is the**difference of two squares**. (the formula is $\displaystyle a^2-b^2=(a-b)(a+b)$

For the denominator, I'm sorry to say it's just a eyeballing...

$\displaystyle 2x^3+3x^2+8x+12={\color{red}2}x^3+{\color{blue}3}x ^2+{\color{red}2}\cdot 4x+{\color{blue}3} \cdot 4$)

Now, you can see some interesting things. If not yet, group the terms with a common factor.

$\displaystyle =2(x^3+4x)+3(x^2+4)$

Factor x in the first term :

$\displaystyle =2x(x^2+4)+3(x^2+4)$ (Surprised)

Do you see it ? The factorisation of the denominator ?