# How do you write the polynomial function with leading coefficient 2, Degree : 3, Zeros : -2, 1, 4?

Jul 9, 2015

$f \left(x\right) = 2 \left(x + 2\right) \left(x - 1\right) \left(x - 4\right)$

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

$= 2 {x}^{3} - 6 {x}^{2} - 12 x + 16$

#### Explanation:

Zeroes correspond to factors. If a cubic has zeroes ${r}_{1}$, ${r}_{2}$ and ${r}_{3}$ and leading coefficient $a$, then it is equal to

$a \left(x - {r}_{1}\right) \left(x - {r}_{2}\right) \left(x - {r}_{3}\right)$