- #1

gabrielh

- 79

- 0

I'm currently taking a Math Analysis class. We started reviewing basic factoring from Algebra 2 before starting new material. I can factor a basic trinomial with the coefficient of x^2 being 1, but if the coefficient is 2 or more, I am not sure how to factor it. I am able to factor these very easily with a graphing calculator, but I'd like to know how to do it by hand.

Factor: 2x^2 + 5x - 12

I know, by using a graphing calculator, that the trinomial factors into (2x-3)(x+4). I know that if the trinomial were, for instance, x^2 - 2x - 8, one could say the product of 8 and the coefficient of x is 8, and the factors of 8 that when added together result in negative 2 are -4 and +2, therefore the factors of x^2 - 2x - 8 are (x-4)(x+2).

Can trinomials with coefficients greater than one be factored in a similar way?

Using the method described above, I come up with a product of 24. Factors of 24 that result in a sum of 5 when added together are +8 and -3, which by the method I am acquainted with would mean the factors are (x+8)(x-3), but that obviously doesn't equal 2x^2 + 5x - 12 when multiplied. I know I'm missing a step somewhere.

Thanks for the help in advance. I know this is a simple question, but it plagued me all day.

## Homework Statement

Factor: 2x^2 + 5x - 12

**2. The attempt at a solution**I know, by using a graphing calculator, that the trinomial factors into (2x-3)(x+4). I know that if the trinomial were, for instance, x^2 - 2x - 8, one could say the product of 8 and the coefficient of x is 8, and the factors of 8 that when added together result in negative 2 are -4 and +2, therefore the factors of x^2 - 2x - 8 are (x-4)(x+2).

Can trinomials with coefficients greater than one be factored in a similar way?

Using the method described above, I come up with a product of 24. Factors of 24 that result in a sum of 5 when added together are +8 and -3, which by the method I am acquainted with would mean the factors are (x+8)(x-3), but that obviously doesn't equal 2x^2 + 5x - 12 when multiplied. I know I'm missing a step somewhere.

Thanks for the help in advance. I know this is a simple question, but it plagued me all day.

Last edited: