document.write( "Question 659398: I know how to factorise equations and solve such as x^2+4x-21=0 already, but Im not sure how to do it when there is a number in front of x^2. For example:
\n" ); document.write( "3b^2+5b+2=0
\n" ); document.write( "How could I factorize and then solve this equation? \n" ); document.write( "

Algebra.Com's Answer #410772 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3b%5E2%2B5b%2B2\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"5\"$ , and the last term is $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"2\"$ to get $\"%283%29%282%29=6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"6\"$ (the previous product) and add to the second coefficient $\"5\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"6\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"6\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*6 = 6
\n" ); document.write( "2*3 = 6
\n" ); document.write( "(-1)*(-6) = 6
\n" ); document.write( "(-2)*(-3) = 6\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"5\"$ :\r
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First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"2\"$ and $\"3\"$ add to $\"5\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"2\"$ and $\"3\"$ both multiply to $\"6\"$ and add to $\"5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"5b\"$ with $\"2b%2B3b\"$ . Remember, $\"2\"$ and $\"3\"$ add to $\"5\"$ . So this shows us that $\"2b%2B3b=5b\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3b%5E2%2Bhighlight%282b%2B3b%29%2B2\"$ Replace the second term $\"5b\"$ with $\"2b%2B3b\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283b%5E2%2B2b%29%2B%283b%2B2%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"b%283b%2B2%29%2B%283b%2B2%29\"$ Factor out the GCF $\"b\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"b%283b%2B2%29%2B1%283b%2B2%29\"$ Factor out $\"1\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28b%2B1%29%283b%2B2%29\"$ Combine like terms. Or factor out the common term $\"3b%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"3b%5E2%2B5b%2B2\"$ factors to $\"%28b%2B1%29%283b%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"3b%5E2%2B5b%2B2=%28b%2B1%29%283b%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "I'll leave the rest to you.\r
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\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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