document.write( "Question 200463: I just help doing some step by step problems can someone show me how to do -30x(squared)+15x + 90 step by step please and 8x(squared)+10x -3 thanks for any help \n" ); document.write( "

Algebra.Com's Answer #150715 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you want to factor these expressions.\r
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\n" ); document.write( "\n" ); document.write( " $\"-30x%5E2%2B15x%2B90\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"-15%282x%5E2-x-6%29\"$ Factor out the GCF $\"-15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"2x%5E2-x-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"2x%5E2-x-6\"$ we can see that the first term is $\"2x%5E2\"$ and the last term is $\"-6\"$ where the coefficients are 2 and -6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient -6 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient -1? Let's list all of the factors of -12:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -12:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,12\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12 ...List the negative factors as well. 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 -12\r
\n" ); document.write( "\n" ); document.write( "(1)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-4)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(6)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(4)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1\r
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First Number	Second Number	Sum
1	-12	1+(-12)=-11
2	-6	2+(-6)=-4
3	-4	3+(-4)=-1
-1	12	-1+12=11
-2	6	-2+6=4
-3	4	-3+4=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 3 and -4 add up to -1 and multiply to -12\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"2x%5E2-x-6\"$ , replace $\"-x\"$ with $\"3x%2B-4x\"$ (notice $\"3x%2B-4x\"$ adds up to $\"-x\"$ . So it is equivalent to $\"-x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%283x%2B-4x%29%2B-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"2x%5E2%2B3x-4x-6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2%2B3x%29%2B%28-4x-6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x%2B3%29-2%282x%2B3%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-2\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-2%29%282x%2B3%29\"$ Since we have a common term of $\"2x%2B3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2B3x-4x-6\"$ factors to $\"%28x-2%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"2x%5E2-x-6\"$ factors to $\"%28x-2%29%282x%2B3%29\"$ (since $\"2x%5E2-x-6\"$ is equivalent to $\"2x%5E2%2B3x-4x-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"-15%282x%5E2-x-6%29\"$ and factors further to $\"-15%28x-2%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"-30x%5E2%2B15x%2B90\"$ completely factors to $\"-15%28x-2%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"8x%5E2%2B10x-3\"$ we can see that the first term is $\"8x%5E2\"$ and the last term is $\"-3\"$ where the coefficients are 8 and -3 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 8 and the last coefficient -3 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient 10? Let's list all of the factors of -24:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -24:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,24\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. 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 -24\r
\n" ); document.write( "\n" ); document.write( "(1)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(24)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(8)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(6)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10\r
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First Number	Second Number	Sum
1	-24	1+(-24)=-23
2	-12	2+(-12)=-10
3	-8	3+(-8)=-5
4	-6	4+(-6)=-2
-1	24	-1+24=23
-2	12	-2+12=10
-3	8	-3+8=5
-4	6	-4+6=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -2 and 12 add up to 10 and multiply to -24\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"8x%5E2%2B10x-3\"$ , replace $\"10x\"$ with $\"-2x%2B12x\"$ (notice $\"-2x%2B12x\"$ adds up to $\"10x\"$ . So it is equivalent to $\"10x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"8x%5E2%2Bhighlight%28-2x%2B12x%29%2B-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"8x%5E2-2x%2B12x-3\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%288x%5E2-2x%29%2B%2812x-3%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%284x-1%29%2B3%284x-1%29\"$ Factor out the GCF of $\"2x\"$ out of the first group. Factor out the GCF of $\"3\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%2B3%29%284x-1%29\"$ Since we have a common term of $\"4x-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"8x%5E2-2x%2B12x-3\"$ factors to $\"%282x%2B3%29%284x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"8x%5E2%2B10x-3\"$ factors to $\"%282x%2B3%29%284x-1%29\"$ (since $\"8x%5E2%2B10x-3\"$ is equivalent to $\"8x%5E2-2x%2B12x-3\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"8x%5E2%2B10x-3\"$ factors to $\"%282x%2B3%29%284x-1%29\"$
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