Final Exam Help:/ ?

May 2010
1
0
Daytona Beach , Florida .
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.
 
Mar 2010
715
381
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 \(\displaystyle q(x) = 0\).
 
  • Like
Reactions: mathFAIL

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
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.
 
  • Like
Reactions: mathFAIL