document.write( "Question 175031: what is equal to x^2-5x+6?\r
\n" ); document.write( "\n" ); document.write( "a. (x-2) (x-3)
\n" ); document.write( "b. (x-2) (x+3)
\n" ); document.write( "c. (x+6) (x-1)
\n" ); document.write( "d. (x-6) (x+1)\r
\n" ); document.write( "\n" ); document.write( "i think the answer is A but I wanted make sure.. thanks :o) \n" ); document.write( "

Algebra.Com's Answer #130128 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-5x%2B6\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-5\"$ , and the last term is $\"6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"6\"$ to get $\"%281%29%286%29=6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"6\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*6
\n" ); document.write( "2*3
\n" ); document.write( "(-1)*(-6)
\n" ); document.write( "(-2)*(-3)\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

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

\r
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-2\"$ and $\"-3\"$ both multiply to $\"6\"$ and add to $\"-5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-5x\"$ with $\"-2x-3x\"$ . Remember, $\"-2\"$ and $\"-3\"$ add to $\"-5\"$ . So this shows us that $\"-2x-3x=-5x\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-2x-3x%29%2B6\"$ Replace the second term $\"-5x\"$ with $\"-2x-3x\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-2x%29%2B%28-3x%2B6%29\"$ Group the terms into two pairs.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29%2B%28-3x%2B6%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29-3%28x-2%29\"$ Factor out $\"3\"$ 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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x-3%29%28x-2%29\"$ Combine like terms. Or factor out the common term $\"x-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-5x%2B6\"$ factors to $\"%28x-3%29%28x-2%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This means that $\"x%5E2-5x%2B6=%28x-3%29%28x-2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%28x-3%29%28x-2%29\"$ to get $\"x%5E2-5x%2B6\"$ or by graphing the original expression and the answer (the two graphs should be identical).
\n" ); document.write( " \n" ); document.write( "

\n" );