How do you write a polynomial function f of least degree that has the following zeroes: 2, 6, -3?

Jan 3, 2017

$f \left(x\right) = {x}^{3} - 8 {x}^{2} - 6 x + 36$

Explanation:

A polynomial function of least degree (that's three) that has the given zeroes would be:

$f \left(x\right) = \left(x - 2\right) \left(x - 6\right) \left(x + 3\right)$

By expanding you get its polynomial form:

${x}^{3} - 2 {x}^{2} - 6 {x}^{2} - 18 x + 12 x + 36$

${x}^{3} - 8 {x}^{2} - 6 x + 36$