Answer:
Yes.
Step-by-step explanation:
To see if h is a factor of f, we can use the factor theorem.
h(x)=x-3 has a zero at x=3 because h(3)=3-3=0.
So we want to see if the zero of h is a zero of f.
Is x=3 a zero of f?
You can check using synthetic division or just plug in 3.
Let's do both.
If you use synthetic you are trying to see if you get a remainder of 0.
If you plug it in you are trying to see if you get 0 as the output when plugging your input 3.
Let's do synthetic first:
Since we are checking to see if x=3 is a zero, that will go on the outside:
3 | 1 -1 -1 -15
| 3 6 15
- ------------------------
1 2 5 0
So yep the remainder is 0 so the answer is yes.
Let's plug it in:
f(3)=3^3-3^2-3-15
f(3)=27-9-3-15
f(3)=18-3-15
f(3)=15-15
f(3)=0
The result is 0 so the answer is yes.
You pick your favorite way here.
