document.write( "Question 1209342: What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(5x^7 - 3x^4 + 10x^2 - 15)? \n" ); document.write( "

Algebra.Com's Answer #848574 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Let,
\n" ); document.write( "f(x) = x^3 + x^2 + x + 1
\n" ); document.write( "g(x) = 5x^7 - 3x^4 + 10x^2 - 15\r
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\n" ); document.write( "\n" ); document.write( "The goal is to find the x^2 coefficient in f(x)*g(x)\r
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\n" ); document.write( "\n" ); document.write( "I'll use the box method\r
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\n" ); document.write( "\n" ); document.write( "Place the terms of f(x) along the top.
\n" ); document.write( "Place the terms of g(x) along the left side.
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	x^3	x^2	x	1
5x^7
-3x^4
10x^2
-15

\r
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\n" ); document.write( "\n" ); document.write( "To fill out this table, we multiply the headers.
\n" ); document.write( "For instance 5x^10 would go in the top left corner (because x^3 times 5x^7 = 5x^10).
\n" ); document.write( "But since 5x^10 isn't an x^2 term, we'll leave this cell blank.\r
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\n" ); document.write( "\n" ); document.write( "We only fill the cells that have x^2 in them
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	x^3	x^2	x	1
5x^7
-3x^4
10x^2				10x^2
-15		-15x^2

\n" ); document.write( "That would be -15x^2 and 10x^2
\n" ); document.write( "They combine to -5x^2\r
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\n" ); document.write( "\n" ); document.write( "Answer: -5
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