document.write( "Question 703190: what binomial of lowest degree must be multiplied to x3-3x2-9x-5 to make it a polynomial with perfect root?
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Algebra.Com's Answer #433357 by KMST(5328) $\"\"$ $\"About$

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The possible rational roots for $\"P%28x%29=x%5E3-3x%5E2-9x-5\"$ are 1, -1, 5, and -5.
\n" ); document.write( " $\"P%28-1%29=%28-1%29%5E3-3%28-1%29%5E2-9%28-1%29-5=-1-3%2B9-5=0\"$ ,
\n" ); document.write( "so $\"-1\"$ is a root of $\"P%28x%29\"$ and
\n" ); document.write( " $\"P%28x%29\"$ has $\"%28x%2B1%29\"$ as a factor.
\n" ); document.write( "Using division (long or synthetic) you find that
\n" ); document.write( " $\"P%28x%29=%28x%5E2-4x-5%29%28x%2B1%29\"$
\n" ); document.write( "Factoring further, since $\"x%5E2-4x-5=%28x-5%29%28x%2B1%29\"$ , you find that
\n" ); document.write( " $\"P%28x%29=%28x-5%29%28x%2B1%29%28x%2B1%29\"$
\n" ); document.write( "So, multiplying times $\"highlight%28%28x-5%29%29\"$ , you would get the perfect square
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\n" ); document.write( "NOTE: I do not like to divide polynomials, so I factor by grouping, like this:
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\n" ); document.write( "(It's also too difficult for me to get terms/coefficients to line up when typing stuff into this website).
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