Answer:
[tex]3 (a-2) (a-5)[/tex]
Step-by-step explanation:
The first step is to find the GCF. Here, it's 3.
[tex]3(a^2-7a+10)[/tex]
Then, you factor the polynomial in the parenthesis.
To find the factors, you will need to find 2 numbers that add to -7, and multiply to 10. -2 and -5 add to -7 and multiply to 10. Now, replace -7a with the factors.
[tex]a^2-2a-5a+10[/tex]
This of this polynomial as 2 problems.
[tex]a^2-2a[/tex] [tex]-5a+10[/tex]
Then, factor again.
[tex]a^2-2a[/tex] [tex]-5a+10[/tex]
[tex]a(a-2)[/tex] [tex]-5(a-5)[/tex]
Then, you keep the factors in parenthesis, and combine the numbers on the outside.
[tex](a-2)(a-5)(a-5)[/tex]
Since, there are 2 of the same factor, you only need one.
[tex](a-2)(a-5)[/tex]
BUT REMEMBER!! In the very beginning, we had a 3 that we took out, we STILL need to add that to the final answer. The final answer is:
[tex]3 (a-2) (a-5)[/tex]
