# Math Help - Final Exam Help:/ ?

1. ## Final Exam Help:/ ?

So my Algebra2 Final exam is on thursday and my teacher was/is none the less incompitent . SO needless to say i'm not doing well in his class , just like every other student he teaches . So my question (out of the many of millions i have) is this:
"GIven the polynomial and one of it's factors, find the remaining factors: 5x^3+12x^2-23x-42;(x-2)"
if anyone could possibly help me with this i would greatly apprieciate it.
-kaye.

2. Since $(x-2)$ is a factor of $f(x) = 5x^3+12x^2-23x-42$, then $5x^3+12x^2-23x-42 = (x-2)q(x)$, for some polynomial $q(x)$. Divide $f(x)$ by $(x-2)$ to find $q(x)$, and then factor the quadratic equation that you find. You will get $(x-2)(x-\alpha)(x-\beta)$ as the required factors, where $\alpha$ and $\beta$ are the roots of the quadratic equation $q(x) = 0$.

3. Originally Posted by mathFAIL
So my Algebra2 Final exam is on thursday and my teacher was/is none the less incompitent . SO needless to say i'm not doing well in his class , just like every other student he teaches . So my question (out of the many of millions i have) is this:
"GIven the polynomial and one of it's factors, find the remaining factors: 5x^3+12x^2-23x-42;(x-2)"
if anyone could possibly help me with this i would greatly apprieciate it.
-kaye.
synthetic division with the known zero ...

Code:
2] .........5..........12.........-23.........-42
......................10...........44..........42
--------------------------------------------------
............5..........22..........21...........0
note the last line represents the coefficients of the depressed polynomial.

the cubic factors as

$y = (x-2)(5x^2 + 22x + 21)$

and the quadratic will also factor ...

$y = (x-2)(5x+7)(x+3)$

you should know how to find the other two zeros.