Question 1173283
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Write the expression of a polynomial function with the following properties:
Zeros:<br>
-2, m=2  -->  two factors of (x+2)
3, m=1  -->  one factor of (x-3)
1, m=2  -->  two factors of (x-1)
0, m=1  -->  one factor of (x)<br>
{{{p(x) = a((x+2)^2)(x-3)((x-1)^2)(x)}}}<br>
Passes through (-1, 32)<br>
Substitute x=-1 to find coefficient a<br>
{{{32 = a(1^2)(-4)((-2)^2)(-1)}}}
{{{32 = 16a}}}
{{{a = 2}}}<br>
The polynomial is<br>
{{{p(x) = 2((x+2)^2)(x-3)((x-1)^2)(x)}}}<br>