x^2+2x-24 =

Question

whats the complete factoring of the trinomial?

Answer 1

To factor this trinomial, first note the leading coefficient is 1 and the constant term is -24.  Now your job is to find two factors of -24 (one must be negative and one must be positive) which add to the coefficient of the linear term (2).  Make note that the coefficient of the linear term is positive - this tells you that the factor 0f -24 which is positive must be the one which is larger in magnitude.  With all of this information you can start making a list of pairs of factors of -24 (only list those where the positive factor is larger in magnitude.

24 x -1

12 x -2

8 x -3

6 x -4

stop here - these are all the factors of -24 where the positive factor is larger in magnitude.

Now add the factors:

24 + -1 = 23

12 - 2 = 10

8 - 3 = 5

6 - 4 = 2  Found them!

Now, to make this process go a little faster you could note that the linear term coefficient being 2 indicates that the factors must be close together.  If you are good at testing the factors in your head, you would quickly see that 6 and -4 are the factors you want.  Otherwise you might start at 8 x -3 and work down to 6 x -4.

 

Now the monomial factors are (x+6)(x-4)

 

long answer to an easy problem, but it shows the logic you should use to solve such problems.

Answer 2

You want 2 factors of -24 that add up to +2. We know that one must be positive and the other negative, because that's the only way to get negative 24 when you multiply them. +6 and -4 would be the correct factors, so the answer is:   (x + 6)(x - 4)