document.write( "Question 71901This question is from textbook Beginning Algebra
\n" ); document.write( ": Please help! \r
\n" ); document.write( "\n" ); document.write( "How do I factor, if possible, the following?\r
\n" ); document.write( "\n" ); document.write( "(a) y^2 + 16y + 64\r
\n" ); document.write( "\n" ); document.write( "(b) by + 7b - 6y - 42\r
\n" ); document.write( "\n" ); document.write( "How do I solve the following for the roots of each quadratic equation?\r
\n" ); document.write( "\n" ); document.write( "(c) x^2 - x - 20 = 0\r
\n" ); document.write( "\n" ); document.write( "(d) 9x^2 = 81\r
\n" ); document.write( "\n" ); document.write( "I have been working on these problems for the past few hours, but can't seem to solve using the right formula. Maybe there is something I am doing wrong.
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Algebra.Com's Answer #51381 by Earlsdon(6294)\"\" \"About 
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Factor:
\n" ); document.write( "(a) \"y%5E2+%2B+16y+%2B+64\" Notice that the first and last terms are perfect squares. This suggests the possibility that the expression itself may be a perfect square. Since \"sqrt%2864%29+=+8\", you can try:
\n" ); document.write( "\"y%5E2%2B16y%2B64+=+%28y%2B8%29%28y%2B8%29\"
\n" ); document.write( "Check using FOIL:
\n" ); document.write( "\"%28y%2B8%29%28y%2B8%29+=+y%5E2%2B8y%2B8y%2B64\" = \"y%5E2%2B16y%2B64\"
\n" ); document.write( "The factors are: \"y%2B8\" and \"y%2B8\"
\n" ); document.write( "(b) \"by%2B7b-6y-42\" Here, you use use \"factor by grouping\". Group the terms as folows:
\n" ); document.write( "\"%28by%2B7b%29+-+%286y%2B42%29\" Notice the change of sign on the last term when the parentheses were added. Now, from each group, factor the common factors.
\n" ); document.write( "\"b%28y%2B7%29+-+6%28y%2B7%29\" Now you can factor the common factor of (y+7)
\n" ); document.write( "\"%28y%2B7%29%28b-6%29\" These are the factors.
\n" ); document.write( "Solve:
\n" ); document.write( "(c) \"x%5E2-x-20+=+0\" This will factor. Notice that the last term has factors of 4 and 5. Also notice that 4-5 = -1 and this is the coefficient of the middle term. So we try:
\n" ); document.write( "\"x%5E2-x-20+=+%28x%2B4%29%28x-5%29\"
\n" ); document.write( "\"%28x%2B4%29%28x-5%29+=+0\" Apply the zero product principle:
\n" ); document.write( "\"x%2B4+=+0\" and/or \"x-5+=+0\"
\n" ); document.write( "If \"x%2B4+=+0\" then \"x+=+-4\"
\n" ); document.write( "If \"x-5+=+0\" then \"x+=+5\"
\n" ); document.write( "The roots are:
\n" ); document.write( "\"x+=+-4\"
\n" ); document.write( "\"x+=+5\"
\n" ); document.write( "(d)
\n" ); document.write( "\"9x%5E2+=+81\" Notice that both sides are perfect squares.
\n" ); document.write( "\"%283x%29%5E2+=+%289%29%5E2\" Take the square root of both sides.
\n" ); document.write( "\"3x+=+sqrt%289%5E2%29\"
\n" ); document.write( "\"3x+=+-9\" or \"3x+=+9\" Divide both sides by 3.
\n" ); document.write( "\"x+=+-3\" or \"x+=+3\"
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