hello I just started on these tonight and i understand all the terms but this one is tricky because it has to go through a specific point and i dont quite understand how to do it yet.
Any help is appreciated:
The polynomial of degree 4, has a root of multiplicity 2 at and roots of multiplicity 1 at and . It goes through the point .
Find a formula for .
My train of thought
(X-4)^2 Multiplicity of 2 and zeros at 4
(X) Multiplicity of 1 and zero at 0
(X+3) Multiplicity of 1 and zero at -3
When i graph it, i get a 4th degree polynominal that goes through (-3,0)(0,0) and bounces off (4,0) but does not go through (5,24) instead it goes through (5,40).