document.write( "Question 317215: Find the zeros of the polynomial function f(x)=x^7−x^5−16x^3+16x and state the multiplicity of each.
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Algebra.Com's Answer #227087 by Fombitz(32388) $\"\"$ $\"About$

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$\"+graph%28+300%2C+300%2C-5%2C5%2C-8%2C8%2C+x%5E7-x%5E5-16x%5E3%2B16x%29+\"$
\n" ); document.write( "As you see from the graph, there are 5 real roots.
\n" ); document.write( "x=-2,-1,0,1,2
\n" ); document.write( "Each root has multiplicity of 1.
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\n" ); document.write( "The polynomial found by these zeros is,
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\n" ); document.write( "Divide the original polynomial by this polynomial to find the quadratic remainder.
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\n" ); document.write( "First factor: $\"x%5E2\"$
\n" ); document.write( " $\"x%5E2%28x%5E5-5x%5E3%2B4x%29=x%5E7-5x%5E5%2B4x%5E3\"$
\n" ); document.write( "Subtract this from the original polynomial to get the remainder,
\n" ); document.write( " $\"%28x%5E7-x%5E5-16x%5E3%2B16x%29-%28x%5E7-5x%5E5%2B4x%5E3%29=4x%5E5-20x%5E3%2B16x\"$
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\n" ); document.write( "Next factor: $\"4\"$
\n" ); document.write( " $\"4%28x%5E5-5x%5E3%2B4x%29=4x%5E5-20x%5E3%2B16x\"$
\n" ); document.write( "Subtract this from the remainder
\n" ); document.write( " $\"%284x%5E5-20x%5E3%2B16x%29-%284x%5E5-20x%5E3%2B16x%29=0\"$
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\n" ); document.write( "So the remainder quadratic is $\"x%5E2%2B4=0\"$ which has complex roots ( $\"-2i\"$ , $\"2i\"$ )
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\n" ); document.write( " $\"x%5E7-x%5E5-16x%5E3%2B16x=%28x%2B2%29%28x%2B1%29x%28x-1%29%28x-2%29%28x%5E2%2B4%29\"$ \n" ); document.write( "

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