Question

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

Can any of the roots have multiplicity?
How can you find a function that has these roots?

Answer 1

The roots cannot have multiplicity because the function is specified as cubic and 3 roots are given.

To find the function, write f(x) = (x – 2)(x – 3)(x – 5), and simplify the right side.

Answer 2

Work backwards to find the factors from the roots, then multiply the factors together.y=x3−10x2+31x−30