Question

Factoring 3 of 11

Answer 1

\[6x^2-x-40\]

Answer 2

a=6
b=-1
c=-40
ac=-240

Answer 3

Looks good so far.

Answer 4

Your goal is to find two numbers that multply to get -(ac), yet add to get +b

Answer 5

-16 and 15

Answer 6

Actually, if it is correct, it would be 16 and -15

Answer 7

Because \(6x^2 -(1)x - 40\). What we replace in parentheses must be positive. So that's why the two numbers are 16 and -15.

Answer 8

I'm trying to help you understand that when finding m and n, b will always be positive

Answer 9

this is where I get lost...
It doesnt make sense to me why it should be though..

Answer 10

Because this is the correct way to do it. What I explained before is slightly off. What I explained before is based on a different method of factoring. This method of factoring works for any factorable expression and it is consistent.

Answer 11

The reason why is because we're only replacing that expression with +b inside the parentheses. We don't deal with the negative until distribution.

Answer 12

I have a headache..

Answer 13

Had I explained it to you initially, you would have understood. I'm sorry you are confused.

Answer 14

It's okay... been a rough month for me...

Answer 15

It's because this method I'm explaining to you is different from what I told you initially. I did not realize you would be confused right now. It's much simpler than you think though. It's not complicated.

Answer 16

\(6x^2 -(\color\green{1}) x - 40\)

Answer 17

As you can tell, I am not the brightest...

Answer 18

No, It's my fault. I didn't explain it correctly the first time and now it's causing all kinds of problems. You're confused about the b value whenever it is negative. But I'm trying to show you a method you can use whether b is positive or negative. And that method is this:

You find two numbers (m and n) that multiply to get ac, yet add to get |b|. In other words, when you find b strictly for this step, it should be positive.

Answer 19

Of course we know that b is sometimes negative, but for just one step in this process, we use the absolute value of b as part of it.

Answer 20

So the formula is:
\(m \times n = ac\)
\(m + n = |b|\)

Answer 21

Once we find that, then we insert \(m + n\) in place of \(|b|\) in the equation.

So in this case, m = 16, n = -15 because
\(16 \times -15 = -240\)
\(16 - 15 = |1| = 1\)

Thus:
\(6x^2 - x - 40\) = \(6x^2 -(\color\green{1})x - 40\)
= \(6x^2 - (\color\green{16 - 15})x - 40\)

Answer 22

And then you continue factoring from there.

Answer 23

AT that point, when you distribute the negative, you'll just need to remember to toggle the signs. If you can handle that, then you should be able to factor virtually mistake free.