SOLUTION: a.The numbers left over from synthetic division make up the remaining factor. In this case, the numbers are 1, -1, and 6. They become the coefficients of the other polynomial. x^2-

Question 826774: a.The numbers left over from synthetic division make up the remaining factor. In this case, the numbers are 1, -1, and 6. They become the coefficients of the other polynomial. x^2-x-6. This gets factored further to find the remaining 2 factors. Find the 2 remaining factors of x^3-3x^2 -4x+12 by factoring x^2-x-6.

b. Find the factors:
x^3-x^2-17x-15=(x+3)( )( )
Any help is much appreciated.

Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
possible solutions are
15,-1,-15,1,-3,5,-5,3
(x+1) (x+3) (x-5)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a.The numbers left over from synthetic division make up the remaining factor. In this case, the numbers are 1, -1, and 6.
They become the coefficients of the other polynomial. x^2-x-6.
This gets factored further to find the remaining 2 factors.
Find the 2 remaining factors of x^3-3x^2 -4x+12 by factoring x^2-x-6.
----
x^2-x-6 = (x-3)(x+2)
b. Find the factors of x^3-x^2 -17x - 15:
-------
-3)....1....-1....-17....-15
....1.....-4....-5...|..0
.
-1).....1...-4..-5
........1...-5..|0
Then x = 5 is a root.
So, x^3-x^2-17x-15=(x+3)(x+1)(x-5)
============
Cheers,
Stan H.
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