Question

Factor completely and then place the factors in the proper location on the grid.

a 2 - a - 20

Answer 1

The fully factored form of this expression would be
(A-5)(A+4).

Answer 2

The correct answer is (a+4)(a-5)

Explanation:

We have the polynomial
`a^2-a-20`

For the polynomials of the form
`ax^2+bx+c` 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).

`a^2-a-20=\\a^2+(-5+4)(a)-20=\\=a^2-5a+4a-20`

Because b=(-5)+4=(-1) and a.c=(-5).4=(-20)

Now we have to factor by grouping:

`a^2-5a+4a-20=\\(a^2+4a)-(5a+20)=\\a(a+4)-5(a+4)=\\=(a-5)(a+4)`

Then, the correct answer is (a+4)(a-5)