Question

Factor: 20a^2-13a-21=0
Please show work. Thanks :)

Answer 1

This is a bit tricky because you have so many possible factor pairs.
You're looking for something like (Ax+B)(Cx+D)
It would multiply out to:
\[ACx^2+(BC+AD)x+BD\]
So in your case AC=20, BD=-21, (BC+AD)=-13

Answer 2

Now look at the factor pairs that can give you -21: 1,21; 3,7 where one of the numbers is negative.
Factor pairs for 20 are: 1,20; 2,10; 4,5
So you can look for combinations of BC+AD that add to -13.

Answer 3

One trick is to look at factors of 420 (20x210) that are 13 apart:
1,2,3,4,5,6,7,10,12,15,20,21,28,30,35,42,60,70,84,105,140,210,420
I probably should have listed them as factor pairs but 15,28 works

Answer 4

We know that AC=20 and AD=-28 so A=4,C=5,D=-7,B=3
(4a+3)(5x-7)

Answer 5

The "trick statement should have read ..."(20x21)"