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You can put this solution on YOUR website!
Here's the trick:
\n" ); document.write( "Multiply the leading coefficient (6) times the independent term (12).
\n" ); document.write( "(Do not worry much about the sign of the product for now).
\n" ); document.write( "I got 72 as the product. How about you?
\n" ); document.write( "Look for factor pairs that multiply to give you that product, and list them.
\n" ); document.write( "I get:
\n" ); document.write( "(1)(72)=72
\n" ); document.write( "(2)(36)=72
\n" ); document.write( "(3)(24)=72
\n" ); document.write( "(4)(18)=72
\n" ); document.write( "(6)(12)=72
\n" ); document.write( "(8)(9)=72
\n" ); document.write( "and no other pair of factors.
\n" ); document.write( "
\n" ); document.write( "OPTIONAL RATIONALE EXPLANATION:
\n" ); document.write( "If the factoring was
\n" ); document.write( "factors of that product,
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "BACK TO THE TRICK (even if you do not understand or do not care for the rationale):
\n" ); document.write( "In the list of factor pairs above, look for factor pairs (consider all sign options now) that add up to the coefficient of the term in x (-17 in the case of the problem you posted) and multiply to give (6)(12)=72 (with its positive sign).
\n" ); document.write( "At this point, you find:
\n" ); document.write( "(-8)(-9)=72=(6)(12)
\n" ); document.write( "and (-8)+(-9)=-17
\n" ); document.write( "Then, -17x could be the result of -8x plus -9x, and you could write the trinomial to be factored as
\n" ); document.write( "
\n" ); document.write( "The expression on the right helps you figure out the factorization.
\n" ); document.write( "All you need now is some creative \"taking out common factors\" trick:
\n" ); document.write( "