What are the zeros of the function?

f(x)=2x^3+6x^2−8x

-1,2, and 4.
-1,0, and 4.
-4,0, and 1.
-4,1, and 2.

The third choice:  -4, 0, and 1

Step-by-step explanation:

Finding zeroes is another way of saying solve...set the equation equal to zero and solve..

0 = 2x³ + 6x² - 8x

0 = 2x(x² + 3x - 4)    (factor out a 2x from all three terms)

0 = 2x(x + 4)(x - 1)       (factor x² + 3x - 4)

So

2x = 0          then x = 0

x + 4 = 0      then x = -4

x - 1 = 0       then x = 1

Our zeroes are -4, 0, and 1

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

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step-by-step explanation: