Answer:
The correct answer is (a+4)(a-5)
Step-by-step explanation:
We have the polynomial [tex]a^2-a-20[/tex]
For the polynomials of the form [tex]ax^2+bx+c[/tex] we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-20 and whose sum is b=(-1).
[tex]a^2-a-20=\\a^2+(-5+4)(a)-20=\\=a^2-5a+4a-20[/tex]
Because b=(-5)+4=(-1) and a.c=(-5).4=(-20)
Now we have to factor by grouping:
[tex]a^2-5a+4a-20=\\(a^2+4a)-(5a+20)=\\a(a+4)-5(a+4)=\\=(a-5)(a+4)[/tex]
Then, the correct answer is (a+4)(a-5)
