Question

Identify the zeros of the polynomial function .

Answer 1

Step-by-step explanation:

To start, every term has an

x

in common, so we can factor that out. Doing this, we get

x

(

x

2

+

x

−

42

)

=

0

What I have in blue can be factored by a thought experiment. What two numbers have a sum of

1

and a product of

−

42

?

After some trial and error, we arrive at

−

6

and

7

. Thus, this business can be factored as

x

(

x

−

6

)

(

x

+

7

)

=

0

We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get

x

=

0

,

x

=

6

, and

x

=

−

7