Question

Find a polynomial function of degree two with 5 as a zero of multiplicity 1 and -4 as a zero of multiplicity 1.

Answer 1

Very straightforward if you know what you are looking for\[y=a(x-5)(x+4)\]with a any nonzero real number.

If a polynomial has a zero at a given value of x (say x=c), then (x-c) is a factor of that polynomial. The multiplicity is the power that factor is raised to. In this case, the multiplicity was one, so each factor was there only once as a factor.

The scaling factor a allows us to stretch or compress the function without changing the roots.