Question

Factor:
x2 + x – 30

I've tried factoring this and I've gotten at least 3 answers but when I go to check them they are not correct. I believe that it is because I am not choosing the right factors. How do I know which factors should go into the parentheses when there is more than one pair?

Answer 1

find two numbers that multiply to -30 AND add to 1

Answer 2

use quadratic formula or find factors of 30 which yeild to 1

Answer 3

The factoring will look like this to start, conceptually, in your mind:

(x )(x )

You can add the plus/minus because there is no coefficient on x^2:

(x + )(x - )

You could do this and be justified because the numeric (-30) is negative. Now, you look for 2 number that when multiplied, give -30 but give +1 when added. Whether it is +1 or -1, we know that they are 1 number apart in absolute value, so we know we are working with:

+5 -6
-5 +6

At this point you know you have:

+6 -5

because they add to +1

Answer 4

The confusing part for a lot of people is, we know now that we have:

(x + 6)(x - 5)

Yet, the "zeros" are -6 and +5

They look "flipped", but we can keep the signs straight conceptually when we realize that the signs in the factors are different from the actual "zeros".

Answer 5

Does that make a little mor sense to you now, @kyland ?

Answer 6

Ah! YES! Thanks so much! Now it makes a lot of sense and I now know what I was doing wrong. Thanks again! :)

Answer 7

Good luck to you in all of your studies and thx for the recognition! @kyland

And you're welcome!