document.write( "Question 1182615: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and. Root of multiplicity 1 at x=-4. The y intercept is y=-9.6
\n" ); document.write( "Find a formula for P(x)
\n" ); document.write( "P(x)= \n" ); document.write( "

Algebra.Com's Answer #812713 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "In the factored form of the polynomial, a root of multiplicity 2 at x=2 means two linear factors of (x-2); a root of multiplicity 1 at x=-4 means one linear factor of (x+4). So the polynomial in factored form is of the form

\n" ); document.write( " $\"P%28x%29=a%28x-2%29%5E2%28x%2B4%29\"$

\n" ); document.write( "To determine the constant factor a, use the given fact that the y-intercept P(0) is -9.6:

\n" ); document.write( " $\"P%280%29=a%28-2%29%5E2%284%29=-9.6\"$
\n" ); document.write( " $\"16a=-9.6\"$
\n" ); document.write( " $\"a=-9.6%2F16=-0.6\"$

\n" ); document.write( "ANSWER: $\"P%28x%29=-0.6%28x-2%29%5E2%28x%2B4%29\"$

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