+2592 I'm reviewing for Semester exams, and forgive me, but i have forgotten how to factor polynomials greater than quadratic. If someone could please help, it would be appreciated. An example given is X4+3X3-12X2-6X+20
+128631 X^4+3X^3-12X^2-6X+20
This might be difficult to factor directly.......we can use the Rational Zeros Theorem to [possibly] reduce the polynomial to one of a 2nd or 3rd degree which might be more easily factored
The possible factors are all the factors of 20 divided by all the factors of 1
1/1 = 1 is not a factor because it does not produce 0 when substituted into the polynomial
-1/1 = -1 is not a factor for the same reason
2/1 = 2 is a factor because we get a 0 when we substitute it into the polynomial
So using synthetic division, we have
2 [ 1 3 - 12 -6 20 ]
2 10 -4 -20
-------------------------------------
1 5 -2 -10 0
So, this reduces the polynomial to
x^3 + 5x - 2x - 10 which factors as
x^2 ( x + 5) - 2(x + 5) =
(x^2 - 2) ( x +5)
So.....the factorization is
(x - 2) (x + 5) (x ^2 - 2)
+43 are you kidding me?! everyone knows how to do that!! jk i have no idea what you are talking about
+128631 X^4+3X^3-12X^2-6X+20
This might be difficult to factor directly.......we can use the Rational Zeros Theorem to [possibly] reduce the polynomial to one of a 2nd or 3rd degree which might be more easily factored
The possible factors are all the factors of 20 divided by all the factors of 1
1/1 = 1 is not a factor because it does not produce 0 when substituted into the polynomial
-1/1 = -1 is not a factor for the same reason
2/1 = 2 is a factor because we get a 0 when we substitute it into the polynomial
So using synthetic division, we have
2 [ 1 3 - 12 -6 20 ]
2 10 -4 -20
-------------------------------------
1 5 -2 -10 0
So, this reduces the polynomial to
x^3 + 5x - 2x - 10 which factors as
x^2 ( x + 5) - 2(x + 5) =
(x^2 - 2) ( x +5)
So.....the factorization is
(x - 2) (x + 5) (x ^2 - 2)
+2592 OH GOD
COMPLETELY FORGOT ABOUT SYNTHETIC DIVISION
YOU JUST SAVED MY EXAM GRADE
Thanks CPhill
+8581 Thanks guys for catching my mistakes today!!! :)
I have not been feeling my 100% best today :'(
+2592 TOOK ya long enough
JK Haley
CPhill, Most just refer to me as Spawn btw
+8581 And here i thought we were starting a beautiful friendship!!
(\_(\
(-.-)
(,,)(,,)
+8581 haha, ohhh.
I may be a blonde, but that does not mean im stupid. :p
Mind is just running slow right now.. ;)
+2592 Didn't mean to imply you were stupid or anything. Sorry
Anyways, i'm calling it a night, got Pre-calc exam and AP exam tomorrow.
Also, my laptop has 20% battery left.
Night CPhill, Melody, and Haley
