document.write( "Question 1037195: Find the zeros of the polynomial function, and state the multiplicity of each.
\n" ); document.write( "f(x)=x^3(x-5)^2(x+9) \n" ); document.write( "

Algebra.Com's Answer #651918 by KMST(5328) $\"\"$ $\"About$

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$\"f%28x%29=x%5E3%28x-5%29%5E2%28x%2B9%29\"$ is given in fully factored form.
\n" ); document.write( "The zeros are the values of $\"x\"$ that make a factor (and hence the product function) zero.
\n" ); document.write( "They are:
\n" ); document.write( " $\"highlight%28x=0%29\"$ , with multiplicity $\"highlight%283%29\"$ ,
\n" ); document.write( "because the factor $\"%28x-0%29=x\"$ appears with the exponent $\"3\"$ in the fully factored expression of $\"f%28x%29\"$ ,
\n" ); document.write( " $\"highlight%28x=5%29\"$ , with multiplicity $\"highlight%282%29\"$ ,
\n" ); document.write( "because the factor $\"%28x-5%29\"$ appears with the exponent $\"2\"$ in the fully factored expression of $\"f%28x%29\"$ , and
\n" ); document.write( " $\"highlight%28x=-9%29\"$ , with multiplicity $\"highlight%281%29\"$ ,
\n" ); document.write( "because the factor $\"%28x-%28-9%29%29=%28x%2B9%29\"$ appears with no exponent
\n" ); document.write( "(which is the same having $\"1\"$ as the exponent)
\n" ); document.write( "in the fully factored expression of $\"f%28x%29\"$ . \n" ); document.write( "

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