# Final Exam Help:/ ?

• May 25th 2010, 04:48 PM
mathFAIL
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.
• May 25th 2010, 05:12 PM
TheCoffeeMachine
Since $\displaystyle (x-2)$ is a factor of $\displaystyle f(x) = 5x^3+12x^2-23x-42$, then $\displaystyle 5x^3+12x^2-23x-42 = (x-2)q(x)$, for some polynomial $\displaystyle q(x)$. Divide $\displaystyle f(x)$ by $\displaystyle (x-2)$ to find $\displaystyle q(x)$, and then factor the quadratic equation that you find. You will get $\displaystyle (x-2)(x-\alpha)(x-\beta)$ as the required factors, where $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the quadratic equation $\displaystyle q(x) = 0$.
• May 25th 2010, 05:17 PM
skeeter
Quote:

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

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

and the quadratic will also factor ...

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

you should know how to find the other two zeros.