document.write( "Question 1065771: c^2+2c-10/10c^2-80c+160 is a rational expression need help factoring completely and finding the domain \n" ); document.write( "

Algebra.Com's Answer #680939 by Theo(13342) $\"\"$ $\"About$

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as far as i can see, the numerator can't be factored manually, so you need to use the quadratic formula to factor it.
\n" ); document.write( "you will get c = -1 plus or minus sqrt(11).
\n" ); document.write( "the denominator can be factors and you will get c = -4 or -4.
\n" ); document.write( "your factored expression will be $\"%28%28c%2B1-sqrt%2811%29%29%2A%28c%2B1%2Bsqrt%2811%29%29%2F%2810%2A%28c-4%29%5E2%29%29\"$
\n" ); document.write( "your domain will be all values of c not equal to 4, because c = 4 would make the denominator equal to 0 which leads to an answer that is undefined.
\n" ); document.write( "you can graph the numerator and denominator separately andt you can graph the full expression to see what they look like.
\n" ); document.write( "my first picture is the graph of the numerator.
\n" ); document.write( "my second picture is the graph of the denominator.
\n" ); document.write( "my third picture is the graph of the numerator divided by the denominator.
\n" ); document.write( "note that sqrt(11) is approximately equal to 3.317 and that -1 - sqrt(11) is approximately equal to -4.317 and that -1 + sqrt(11) is approximately equal to 2.317 as shown on the first picture.
\n" ); document.write( "that's where the numerator crosses the x-axis.
\n" ); document.write( "4 is where the denominator touches the x-axis.
\n" ); document.write( "4 is where the asymptote is when you divide the numerator by the denominator.
\n" ); document.write( "to graph this expression, i changed c to x because most graphing software require the horizontal axis to be x and the vertical axis to be y.
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