document.write( "Question 1174668: For what values of t can 10x^2+tx+8 be written as the product of two binomials?\r
\n" ); document.write( "\n" ); document.write( "I don't really get what we're supposed to do in this question. Please explain. \n" ); document.write( "

Algebra.Com's Answer #800127 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"10x%5E2%2Btx%2B8+\"$ \r
\n" ); document.write( "\n" ); document.write( "compare to $\"ax%5E2%2Bbx%2Bc\"$ , => $\"+a=10\"$ , $\"b=t\"$ , and $\"c=8\"$ \r
\n" ); document.write( "\n" ); document.write( "you need\r
\n" ); document.write( "\n" ); document.write( " $\"ac=10%2A8=80\"$ \r
\n" ); document.write( "\n" ); document.write( "factors of $\"80\"$ are:± $\"1\"$ | ± $\"2\"$ | ± $\"4+\"$ | ± $\"5\"$ | ± $\"8+\"$ | ± $\"10\"$ | ± $\"16+\"$ | ± $\"20\"$ | ± $\"40\"$ | ± $\"80+\"$ \r
\n" ); document.write( "\n" ); document.write( "following sums are potential values for $\"t\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1%2B80=81\"$
\n" ); document.write( " $\"2%2B40=42\"$
\n" ); document.write( " $\"4%2B20=24\"$
\n" ); document.write( " $\"5%2B16=21\"$
\n" ); document.write( " $\"8%2B10=18\"$ \r
\n" ); document.write( "\n" ); document.write( "same is with negative values
\n" ); document.write( "
\n" ); document.write( "so $\"t\"$ = ± $\"18\"$ ,± $\"21\"$ ,± $\"24\"$ ,± $\"42\"$ ,± $\"81\"$ \r
\n" ); document.write( "\n" ); document.write( "check some:\r
\n" ); document.write( "\n" ); document.write( " $\"t\"$ = ± $\"18\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"t=+18%7D%7D+we+have%0D%0A%0D%0A%7B%7B%7B10x%5E2%2B18x%2B8\"$ ....we can write $\"18x\"$ as $\"10x+%2B8x\"$
\n" ); document.write( " $\"10x%5E2%2B10x+%2B8x%2B8\"$ ...group
\n" ); document.write( " $\"%2810x%5E2%2B10x%29+%2B%288x%2B8%29\"$
\n" ); document.write( " $\"10x%28x%2B1%29+%2B8%28x%2B1%29\"$
\n" ); document.write( " $\"%2810x+%2B8%29%28x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"t=-18\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10x%5E2-18x%2B8%7B%7B%7B+....we+can+write+%7B%7B%7B-18x+\"$ as $\"-10x+-8x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10x%5E2-10x+-8x%2B8\"$ ...group
\n" ); document.write( " $\"%2810x%5E2-10x%29+-%288x-8%29\"$
\n" ); document.write( " $\"10x%28x-1%29+-8%28x-1%29\"$
\n" ); document.write( " $\"%2810x+-8%29%28x-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"t\"$ = ± $\"21\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"t=21+\"$ which can be written as $\"16%2B5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10x%5E2%2B21x%2B+8\"$
\n" ); document.write( " $\"10x%5E2%2B16x%2B5x%2B+8\"$
\n" ); document.write( " $\"%2810x%5E2%2B16x%29%2B%285x%2B+8%29\"$
\n" ); document.write( " $\"2x%285x%2B8%29%2B%285x%2B+8%29\"$
\n" ); document.write( " $\"%282x+%2B+1%29+%285x+%2B+8%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " do same using $\"t=-21\"$ , and you will get $\"%282+x+-+1%29+%285+x+-+8%29+\"$ \r
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