document.write( "Question 620914: Using complete sentences, explain how to factor each one. Be sure that the final factorization (or \"answer\") is a part of your explanation. \r
\n" ); document.write( "\n" ); document.write( "10x2 − 7x − 3 \n" ); document.write( "

Algebra.Com's Answer #390505 by KMST(5328) $\"\"$ $\"About$

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This is how I do it.
\n" ); document.write( "To factor the quadratic trinomial $\"10x%5E2-7x-3\"$ ,
\n" ); document.write( "I first multiply together the absolute values of the leading coefficient (10) and the independent term (-3) to get $\"10%2A3=30\"$ .
\n" ); document.write( "I look for, and list all pairs of factors that multiply to yield that product, and find 4 such pairs:
\n" ); document.write( " $\"1%2A30=30\"$
\n" ); document.write( " $\"2%2A15=30\"$
\n" ); document.write( " $\"3%2A10=30\"$
\n" ); document.write( " $\"5%2A6=30\"$ .
\n" ); document.write( "One of those pairs will be the absolute values of the coefficients of first degree terms obtained when multiplying the final factorization.
\n" ); document.write( "Because the independent term (-3) is negative, I know that those coefficients of first degree terms have opposite signs.
\n" ); document.write( "I also know that they add up to the coefficient of the first degree term in the original polynomial (-7).
\n" ); document.write( "From the four pairs of factors found above, the pair of factors, with signs, that add up to -7 is
\n" ); document.write( " $\"-10%2B3=-7\"$ .
\n" ); document.write( "The expanded product of the factorization will contain $\"-10x\"$ and $\"%2B3x\"$ in addition to the leading and independent terms $\"10x%5E2\"$ and $\"-3\"$ .
\n" ); document.write( "I then organize the expanded product of the factorization in a 2 by 2 square, with the newly found terms at opposite corners:
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\n" ); document.write( "Next, I look for common factors for each row and column and write them on the same row/column, outside the square.
\n" ); document.write( "I find $\"10x\"$ as a common factor for $\"10x%5E2\"$ and $\"-10x\"$ , so I write $\"10x\"$ to the left of $\"10x%5E2\"$ .
\n" ); document.write( "I find $\"3\"$ as a common factor for $\"3x\"$ and $\"-3\"$ , so I write $\"3\"$ to the left of $\"3x\"$ .
\n" ); document.write( "I write $\"x\"$ above $\"10x%5E2\"$ and $\"-10x\"$ , because it is their common factor.
\n" ); document.write( "I write $\"-1\"$ above $\"-10x\"$ and $\"-3\"$ , because it is their common factor.
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\n" ); document.write( "Now I make a binomial of the terms written above the square $\"x-1\"$ and another binomial with the terms written to the left of the square $\"10x%2B3\"$ .
\n" ); document.write( "I multiply those binomials to verify that the terms inside the square are generated.
\n" ); document.write( "I also verify that collecting terms in that product produces the original trinomial.
\n" ); document.write( " $\"%2810x%2B3%29%28x-1%29=10x%5E2-10x%2B3x-3=10x%5E2-7x-3\"$ \n" ); document.write( "

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