SOLUTION: page 330 # 64 - factor each polynomial x^2 - 5xs -24s^2

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Question 104687: page 330 # 64 - factor each polynomial
x^2 - 5xs -24s^2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
We want to find the values for a and b that make this true.
x%5E2+-+5sx+-24s%5E2=%28x%2Ba%29%28x%2Bb%29
If we expand the equation in terms of a and b, we can find what relationships need to be met to solve the problem.
Note, the terms a and b will also include an s term for each.
Don't let that throw you off, it acts like a constant.
%28x%2Ba%29%28x%2Bb%29=x%5E2%2B%28a%2Bb%29x%2Bab
Let's compare terms in the original equation:
1.+%28a%2Bb%29x=-5sx or
a%2Bb+=-5s
2.ab=-24s%5E2
Let's use equation 2 and look for factors of -24s%5E2 that when summed equal -5s (Equation 1).
Integer factors of 24s%5E2 are (1s,24s),(2s,12s),(3s,8s),(4s,6s).
(3s,8s) looks promising since their difference is 5s.
Now we need to get the signs right.
-8s%2B3s=-5s and %28-8s%29%283s%29=-24s%5E2
x%5E2+-+5sx+-24s%5E2=%28x-8s%29%28x%2B3s%29