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

$x^2-16=0\iff x^2=16 \iff x=\pm\sqrt{16}=\pm 4$

or

$x-3=0\iff x=3$

Answer 2

Answer:

x = - 4, 0, 3, 4

Step-by-step 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