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Question

The polynomial of degree 4, P(x)P(x) has a root of multiplicity 2 at x=2x=2 and roots of multiplicity 1 at x=0x=0 and x=−3x=-3. It goes through the point (5,216)(5,216).

Find a formula for P(x)P(x).

Answer 1

From the zeros, you can write that the polynomial has to be in the form:

p(x) = a(x-2)²(x)(x+3) so that a(x-2)²(x)(x+3) will be equal to 0 for the zeroes of p(x)

Now, solve for a so that p(5) = 216

a(3)²(5)(8) = 216 and a = .6

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