SOLUTION: Hello, I'm not sure where this problem is supposed to go so I just put it here. Use synthetic division to show that x=7 is a root of the equation x^3-9x^2-1x+105=0. Then, use t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hello, I'm not sure where this problem is supposed to go so I just put it here. Use synthetic division to show that x=7 is a root of the equation x^3-9x^2-1x+105=0. Then, use t      Log On

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Question 922845: Hello, I'm not sure where this problem is supposed to go so I just put it here.
Use synthetic division to show that x=7 is a root of the equation x^3-9x^2-1x+105=0.
Then, use the result to factor the polynomial completely into the form (x+A)(x+B)(x+C).
thank you in advance!
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial was made using binomial factors. When they were multiplied and the result simplified and put into general form, the result became x%5E3-9x%5E2-1x%2B105.

Now, you want to test for different possible binomial factors to see which ones are pefect divisors of the polynomial, meaning the remainder is zero. You are guided with the instruction to first test the root x=7, which corresponds to the binomial factor of x-7.

_______7_____|______1______-9______-1________105
_____________|_
_____________|_____________7_______-14_______-105
_____________|_______________________________________
____________________1_______-2_____-15________0


The remainder is 0; x=7 is a root of the given polynomial.
The resulting quotient means that the quotient is really x%5E2-2x-15, which you will either factor if possible and you can find the combination or use general solution for quadratic formula.

Simple factoring trials should be enough %28x%2B3%29%28x-5%29=0=x%5E2-2x-15

The factorization for the given equation is highlight%28%28x-7%29%28x-5%29%28x%2B3%29=0%29 or any arrangement equivalent according to commutative property for multiplication.