Polynomial Function

Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-2. It goes through the point (5,21).
Find a formula for P(x) ?

Answer 1

Given the roots the factors can be determined:

 

P(x) = a(x - 4)(x - 4)(x - 0)( x + 2), where a = learning coefficient.

 

Multiply this out to get the polynomial. To determine the value of a:

 

21 = a(5 - 4)(5 - 4)(5 - 0)(5 + 2)

21 = a (1)(1)(5)(7)

21 = 35a

21/35 = a

3/5 = a

Answer 2

Hi Sally,

 

I agree with Mark, except that the a = the leading coefficient (not the learning coefficient).  Did that make sense to you?