# How do you find all the zeros of f(x) = 4(x-3)(x+6)^3 ?

Jan 2, 2018

$x = 3$ and $x = - 6$ are zeroes to this polynomial function. Try plugging the zeroes into the function and $f \left(x\right)$ will evaluate to 0.

#### Explanation:

Zeroes of a function are values that make $f \left(x\right) = 0$. If three terms are being multiplied and the product is 0, at least one of the terms has to be equal to 0.

Let's set $x - 3$ equal to zero:

$x - 3 = 0$

• Add 3 to both sides

$\implies x = 3$ (this is one of our zeroes)

Let's set ${\left(x + 6\right)}^{3}$ equal to zero

${\left(x + 6\right)}^{3} = 0$

• Take the cube root of both sides (cube root of zero is zero)

$\implies x + 6 = 0$

• Subtract 6 from both sides

$\implies x = - 6$ (this is our second zero to our function)