document.write( "Question 303320: Need help with trinomials! Any guidance on this set would be GREATLY appreciated!!
\n" ); document.write( "3. a) Factor completely.
\n" ); document.write( "v^3-5v^2-36v\r
\n" ); document.write( "\n" ); document.write( " b)Solve and simplify:
\n" ); document.write( "r^2+3r-18=0
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\n" ); document.write( " c)Solve for the solution set.
\n" ); document.write( "(x+9)(x-13)(x+6)>0\r
\n" ); document.write( "\n" ); document.write( " d)Factor completely:
\n" ); document.write( "c^2+4c+4\r
\n" ); document.write( "\n" ); document.write( " e)Factor completely in factored form:
\n" ); document.write( "3x^7-15x^6+24x^5\r
\n" ); document.write( "\n" ); document.write( " f)Multiply
\n" ); document.write( "(-3n)^2 * (4n^9)^2\r
\n" ); document.write( "\n" ); document.write( "Thank you so much for your help! \n" ); document.write( "

Algebra.Com's Answer #217435 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first two to get you started. Please only post one problem at a time.\r
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\n" ); document.write( "\n" ); document.write( "a)\r
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\n" ); document.write( "\n" ); document.write( " $\"v%5E3-5v%5E2-36v\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"v%28v%5E2-5v-36%29\"$ Factor out the GCF $\"v\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"v%5E2-5v-36\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"v%5E2-5v-36\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-5\"$ , and the last term is $\"-36\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-36\"$ to get $\"%281%29%28-36%29=-36\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-36\"$ (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 $\"-36\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-36\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,9,12,18,36\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-9,-12,-18,-36\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 $\"-36\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-36) = -36
\n" ); document.write( "2*(-18) = -36
\n" ); document.write( "3*(-12) = -36
\n" ); document.write( "4*(-9) = -36
\n" ); document.write( "6*(-6) = -36
\n" ); document.write( "(-1)*(36) = -36
\n" ); document.write( "(-2)*(18) = -36
\n" ); document.write( "(-3)*(12) = -36
\n" ); document.write( "(-4)*(9) = -36
\n" ); document.write( "(-6)*(6) = -36\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	-36	1+(-36)=-35
2	-18	2+(-18)=-16
3	-12	3+(-12)=-9
4	-9	4+(-9)=-5
6	-6	6+(-6)=0
-1	36	-1+36=35
-2	18	-2+18=16
-3	12	-3+12=9
-4	9	-4+9=5
-6	6	-6+6=0

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"4\"$ and $\"-9\"$ add to $\"-5\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"4\"$ and $\"-9\"$ both multiply to $\"-36\"$ and add to $\"-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-5v\"$ with $\"4v-9v\"$ . Remember, $\"4\"$ and $\"-9\"$ add to $\"-5\"$ . So this shows us that $\"4v-9v=-5v\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"v%5E2%2Bhighlight%284v-9v%29-36\"$ Replace the second term $\"-5v\"$ with $\"4v-9v\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28v%5E2%2B4v%29%2B%28-9v-36%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"v%28v%2B4%29%2B%28-9v-36%29\"$ Factor out the GCF $\"v\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"v%28v%2B4%29-9%28v%2B4%29\"$ Factor out $\"9\"$ 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( " $\"%28v-9%29%28v%2B4%29\"$ Combine like terms. Or factor out the common term $\"v%2B4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"v%28v%5E2-5v-36%29\"$ then factors further to $\"v%28v-9%29%28v%2B4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"v%5E3-5v%5E2-36v\"$ completely factors to $\"v%28v-9%29%28v%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"v%5E3-5v%5E2-36v=v%28v-9%29%28v%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"v%28v-9%29%28v%2B4%29\"$ to get $\"v%5E3-5v%5E2-36v\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "b)\r
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\n" ); document.write( "\n" ); document.write( " $\"r%5E2%2B3r-18=0\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"%28r%2B6%29%28r-3%29=0\"$ Factor the left side \r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
\n" ); document.write( "\n" ); document.write( " $\"r%2B6=0\"$ or $\"r-3=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"r=-6\"$ or $\"r=3\"$ Now solve for r in each case\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are $\"r=-6\"$ or $\"r=3\"$ \n" ); document.write( "

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