Question

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

Answer 1

`2x^2+12x+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 = aq + 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+12x+3`

and `r = 57x+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:
`(x^2-4) * 2x^2 = 2x^4-8x^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.