Find the value of the missing piece!! :)

Our x-intercepts are at:

Our y-intercept is (0, -10).

Step-by-step explanation:

We have the function:

And we know that one factor is:

Since we know one factor, we can use synthetic division to find the depressed polynomial, then continue factoring to find the remaining zeros (x-intercepts).

To find the y-intercept, we can simply substitute 0 for x and evaluate. This can be done anytime.

We can apply synthetic division for a polynomial P(x) divided by a binomial in the form (x-a).

Since our factor is (x-5), a=5.

Please refer to the attachment below for the synthetic division.

So, we are left with:

The remaining factor is now a quadratic. This can be easily factored:

To find our zeros, set our function f(x) to 0:

Then by the Zero Product Property:

Hence, our x-intercepts are:

To find our y-intercept, we can substitute 0 for x and evaluate. Hence:

Evaluate:

So, our y-intercept is at (0, -10).