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4 votes
X2 - x - 6 =

Simplified. I know the answer is (x+2)(x-3), but I don't understand how the answer was achieved. Can I please get an explanation of this?

2 Answers

3 votes
I had a lot of trouble with this when my algebra class started doing it,
a long time ago.

The key is this: Look at the -6 at the end. You have to find two factors
of that number that add up to the -1 in the middle.

Here are the possible factors of -6 :

-1 ... 6
+1 ... -6
-2 ... 3
+2 ... -3

Can you find a pair on the list that adds up to -1 ?
How about +2 and -3 ?
Their product is -6 and their sum is -1. That's what you need.

Now set up a couple of binomial factors like this: (x....) (x....)
and write in the pair of numbers you found: (x + 2) (x - 3)
That's the factored form of the original expression.


User ZILONG PAN
by
8.5k points
2 votes

x^2-x-6=(x+2)(x-3)\\\\-x=2x-3x\\-6=2*(-3)\\\\or\\\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)
User Tobias Geiselmann
by
7.0k points

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