# How do you divide (2x^4+12x^3-5x^2+9x+3)/(x^2-4) ?

May 11, 2018

$2 {x}^{2} + 12 x + 3$

#### Explanation:

Using Division Euclid's with said to us is always possible to divide a number for other same him having rest, then:
$b = a q + r$ , com $r < a .$

b = 2x^4+12x^3−5x^2+9x+3
a = x^2−4

using $q$ for to know how to go in b, we'll have $q = {x}^{2} + 12 x + 3$

and $r = 57 x + 15$

Like this, 2x^4+12x^3−5x^2+9x+3 = (x^2−4)(x^2+12x+3)+ (57x+15)

Simplifying, for to find q you'll have to test the possibilities for each term of b, for example:
$\left({x}^{2} - 4\right) \cdot 2 {x}^{2} = 2 {x}^{4} - 8 {x}^{2}$ , this result is the first term is b and more something each we'll subtraction in b, and this process will to repeat until us can't do it more.