Question

Find the zeros of the following function, and plot them on the graph.

Answer 1

The zeros are -6, -4, 3 and 4

Explanation:

In order to find the zeros of a function we have to:

• Set the function equal to 0
• Factor it
• Set each one of the factors equal to 0
• Solve for x for each one of those factors.

Finding the zeros.

We can start setting the function equal to 0

`f(x) = 0`

For this exercise we have

`(x^2-16)(x^2+3x-18)=0`

Then we can factor each parenthesis.

For the first one we have a difference of squares, so we can use
`a^2-b^2 =(a-b)(a+b)`, which will give us

`(x-4)(x+4)(x^2+3x-18)=0`

For the last parenthesis, we need to think of a couple of numbers that multiplied give us the last number which is -18 and the sum give us the middle coefficient which is +3, those numbers are +6 and -3, since +6*(-3) = -18 and their sum give us 3.

`(x-4)(x+4)(x+6)(x-3)=0`

Then we can set each one of those factors equal to 0.

`x-4=0,        x+4=0,     x+6=0, x-3=0`

So we can solve for x for each, which will give us

`x=4, x= -4, x = -6, x = 3`

Thus the zeros are -6, -4, 3, 4.

And we can plot them as you can see on the attached image, just click on dots and select (-6,0), (-4,0), (3,0) and (4,0). The sketch will look like the following image.