document.write( "Question 642394: 70s^2-165sr+90r^2 factor trinomial completely
\n" ); document.write( "answer I had was 5
\n" ); document.write( "5(2a-3(7a-6r) but my answer was wrong please help\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #404089 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"70s%5E2-165sr%2B90r%5E2\" Start with the given expression.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5%2814s%5E2-33rs%2B18r%5E2%29\" Factor out the GCF \"5\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression \"14s%5E2-33rs%2B18r%5E2\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Looking at the expression \"14s%5E2-33rs%2B18r%5E2\", we can see that the first coefficient is \"14\", the second coefficient is \"-33\", and the last coefficient is \"18\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient \"14\" by the last coefficient \"18\" to get \"%2814%29%2818%29=252\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to \"252\" (the previous product) and add to the second coefficient \"-33\"?\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 \"252\" (the previous product).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of \"252\":\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-7,-9,-12,-14,-18,-21,-28,-36,-42,-63,-84,-126,-252\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 \"252\".\r
\n" ); document.write( "\n" ); document.write( "1*252 = 252
\n" ); document.write( "2*126 = 252
\n" ); document.write( "3*84 = 252
\n" ); document.write( "4*63 = 252
\n" ); document.write( "6*42 = 252
\n" ); document.write( "7*36 = 252
\n" ); document.write( "9*28 = 252
\n" ); document.write( "12*21 = 252
\n" ); document.write( "14*18 = 252
\n" ); document.write( "(-1)*(-252) = 252
\n" ); document.write( "(-2)*(-126) = 252
\n" ); document.write( "(-3)*(-84) = 252
\n" ); document.write( "(-4)*(-63) = 252
\n" ); document.write( "(-6)*(-42) = 252
\n" ); document.write( "(-7)*(-36) = 252
\n" ); document.write( "(-9)*(-28) = 252
\n" ); document.write( "(-12)*(-21) = 252
\n" ); document.write( "(-14)*(-18) = 252\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 \"-33\":\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "
First NumberSecond NumberSum
12521+252=253
21262+126=128
3843+84=87
4634+63=67
6426+42=48
7367+36=43
9289+28=37
122112+21=33
141814+18=32
-1-252-1+(-252)=-253
-2-126-2+(-126)=-128
-3-84-3+(-84)=-87
-4-63-4+(-63)=-67
-6-42-6+(-42)=-48
-7-36-7+(-36)=-43
-9-28-9+(-28)=-37
-12-21-12+(-21)=-33
-14-18-14+(-18)=-32
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers \"-12\" and \"-21\" add to \"-33\" (the middle coefficient).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the two numbers \"-12\" and \"-21\" both multiply to \"252\" and add to \"-33\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now replace the middle term \"-33rs\" with \"-12rs-21rs\". Remember, \"-12\" and \"-21\" add to \"-33\". So this shows us that \"-12rs-21rs=-33rs\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"14s%5E2%2Bhighlight%28-12rs-21rs%29%2B18r%5E2\" Replace the second term \"-33rs\" with \"-12rs-21rs\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%2814s%5E2-12rs%29%2B%28-21rs%2B18r%5E2%29\" Group the terms into two pairs.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2s%287s-6r%29%2B%28-21rs%2B18r%5E2%29\" Factor out the GCF \"2s\" from the first group.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2s%287s-6r%29-3r%287s-6r%29\" Factor out \"2s\" from the second group.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%282s-3r%29%287s-6r%29\" Factor out \"7s-6r\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So \"14s%5E2-33rs%2B18r%5E2\" factors to \"%282s-3r%29%287s-6r%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "this means \"5%2814s%5E2-33rs%2B18r%5E2%29\" factors to \"5%282s-3r%29%287s-6r%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the final answer is \"5%282s-3r%29%287s-6r%29\" \n" ); document.write( "
\n" );