document.write( "Question 1099933: 10x^5+11x^4+3x^3 I have to factor by grouping and ac method please help I don’t know what I’m doing wrong \n" ); document.write( "

Algebra.Com's Answer #714460 by KMST(5328) $\"\"$ $\"About$

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First step - take out common factors:
\n" ); document.write( " $\"10x%5E5%2B11x%5E4%2B3x%5E3=x%5E3%2810x%5E2%2B11x%2B3%29\"$
\n" ); document.write( "
\n" ); document.write( "Now you have to factor $\"10x%5E2%2B11x%2B3\"$ .
\n" ); document.write( "I assume you were told that you could split the middle term into two terms,
\n" ); document.write( "and then \"factor by grouping\",
\n" ); document.write( "finding the coefficients of the split terms as factors of $\"ac\"$ ,
\n" ); document.write( "where $\"a\"$ is the coefficient of $\"x%5E2\"$ and $\"c\"$ is the independent term.
\n" ); document.write( " $\"a=10\"$ and $\"c=3\"$ , so $\"ac=10%2A3=30\"$ .
\n" ); document.write( "You want to find a pair of numbers (factors of 30)
\n" ); document.write( "whose product is $\"30\"$ , and whose sum is $\"11\"$ .
\n" ); document.write( "Because the product and the sum are positive,
\n" ); document.write( "you know that the two factors are positive.
\n" ); document.write( "Nice, we do not have to worry about negative numbers.
\n" ); document.write( "The pairs of numbers that give $\"30\"$ as a product are
\n" ); document.write( " $\"1%2A30=30\"$ ,
\n" ); document.write( " $\"2%2A15=30\"$ ,
\n" ); document.write( " $\"3%2A10=30\"$ , and
\n" ); document.write( " $\"5%2A6=30\"$ .
\n" ); document.write( "So, we pick $\"5\"$ and $\"6\"$ ,
\n" ); document.write( "because they add to the middle term: $\"5%2B6=11\"$ .
\n" ); document.write( "Writing only the part to be factored,
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.
\n" ); document.write( "So, after all that work,
\n" ); document.write( " $\"10x%5E5%2B11x%5E4%2B3x%5E3=highlight%28x%5E3%285x%2B3%29%282x%2B1%29%29\"$ . \n" ); document.write( "

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