Find a polynomial of degree 3 whose roots are 0,1,3 and so thay f(2)=10

Question

Find a polynomial of degree 3 whose roots are 0,1,3 and so thay f(2)=10

I have no idea how to solve this and the tutors in my school are no help, can anyone here help me?

Answer 1

If 0,1,and 3 are roots, then x, (x-1) , and (x-3) are factors of the polynomial function.

To get the function to pass through (2,10) there are choices.

The most straightforward: let f(x) = A(x)(x-1)(x-3). Then plug 2 for x, 10 for f(x) and solve for A.

You can choose to multiply all those factors together to convince yourself degree is 3.