document.write( "Question 104687: page 330 # 64 - factor each polynomial
\n" ); document.write( "x^2 - 5xs -24s^2 \n" ); document.write( "

Algebra.Com's Answer #76216 by Fombitz(32388) $\"\"$ $\"About$

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

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