Question 1182615
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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<br>
{{{P(x)=a(x-2)^2(x+4)}}}<br>
To determine the constant factor a, use the given fact that the y-intercept P(0) is -9.6:<br>
{{{P(0)=a(-2)^2(4)=-9.6}}}
{{{16a=-9.6}}}
{{{a=-9.6/16=-0.6}}}<br>
ANSWER: {{{P(x)=-0.6(x-2)^2(x+4)}}}<br>