Question

GUYS PLEASE HELP ME OUT

Answer 1

A multiplication equals zero if and only if at least one of the factors is zero. In this case, the factors are
`5x`,
`x^2-16`,
`x-3`. So, the equation equals zero if and only if

`5x=0\iff x=0`

or

`x^2-16=0\iff x^2=16 \iff x=\pm√(16)=\pm 4`

or

`x-3=0\iff x=3`

Answer 2

x = - 4, 0, 3, 4

Explanation:

Given

f(x) = - 5x(x² - 16)(x - 3) ← x² - 16 is a difference of squares, thus

f(x) = - 5x(x - 4)(x + 4)(x - 3)

To find the zeros, equate f(x) to zero, that is

- 5x(x - 4)(x + 4)(x - 3) = 0

Equate each factor to zero and solve for x

- 5x = 0 ⇒ x = 0

x - 4 = 0 ⇒ x = 4

x + 4 = 0 ⇒ x = - 4

x - 3 = 0 ⇒ x = 3

Thus the zeros are

x = - 4, x = 0, x = 3, x = 4