# Final Exam Help:/ ?

#### 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.

#### 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 $$\displaystyle q(x) = 0$$.

• mathFAIL

#### skeeter

MHF Helper
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.

• mathFAIL