# Thread: polynomial division + simultaneous equations + other :S

1. ## polynomial division + simultaneous equations + other :S

Sorry about ridiculous title, but i wasnt sure ....

1) it is given that $f(x)= xcubed+3xsquared-6x-8$ (having large problems with the maths layout thing)

hence express $f(x)$ as a product of 3 linear factors

2)Solve $4a+2b+12=0$and $a-b+3=0$

The 0's are really throwing me on this one :S

2. 1. $f(x) = x^3 + 3x^2 - 6x - 8$

Try factoring out $x - 2$.

$x^2(x - 2) = x^3 - 2x^2$

$x^3 + 3x^2 - 6x - 8$
$-(x^3 - 2x^2)$
$= 5x^2 - 6x - 8$

$5x(x - 2) = 5x^2 - 10x$

$5x^2 - 6x - 8$
$-(5x^2 - 10x)$
$= 4x - 8$

$4(x - 2) = 4x - 8$

$4x - 8$
$-(4x - 8)$
$= 0$

$\frac{x^3 + 3x^2 - 6x - 8}{x - 2} = x^2 + 5x + 4$

$x^3 + 3x^2 - 6x - 8 = (x - 2)(x^2 + 5x + 4) = (x - 2)(x + 1)(x + 4)$

2. Change the system to
$4a + 2b = -12$
$a - b = -3$.

Multiplying the second equation by 2 yields
$4a + 2b = -12$
$2a - 2b = -6$

$6a = -18$.

Can you finish?

3. 1st one = wow! so complicated

2nd one = i feel stupid :P

Thanks so much

4. The process I used for solving the first problem is known as long division of polynomials (and a little bit of factoring). For polynomials of degree 3 or greater, you will have to try dividing the polynomial by different factors using either this method or synthetic division, which is basically a symbolic representation of long division.