how do you factor 3x^2 - 5x - 12?

Factor by grouping.

1) First, multiply the coefficient of the x^2 term by the constant: 3(-12) = -36
2) Find factors of -36 that will add to -5(from the middle term -5x).

3) The factors of -36 that add to -5 are -9 and + 4.

4)Rewrite the -5x term using -9 and + 4: 3x^2 - 9x + 4x - 12

5)Group the four terms two at a time: (3x^2 - 9x) + (4x - 12)

6)Factor the common factor from each: 3x(x - 3) +4(x - 3)

7)Factor the common factor in the parenthesis: (x - 3)(3x + 4)

There you go. Hope this helped.

(3x + 4)(x - 3)

1. Use a graphing calculator: go to y= and type 3x^2 - 5x - 12.
2. Use quadratic formula. x=(-b+ or- square root bsquared -4ac)/2a

3x^2 - 5x - 12
= (3x + 4)(x - 3)

Well, since 3 is a prime number as the coefficient in the square factor, that limits the number of possibilities.

(3x + m)(x + n)

Now, you have to find m and n.

You know that m*n = -12, and m+3n = -5

Substituting m for n in the 2nd equation: m + 3(-12/m) = -5

multiply through by m: m^2 +5m - 36 = 0
Factoring this yields (m-4)(m+9)=0 so m = 4,-9

-9 is not a factor of 12 so that is not a possible solution

So, m = 4 and use substitution to get n = -3

Now, substitute back into the factor (3x + m)(x + n)

Answer:
(3x + 4)(x - 3)

3x² has only one way you can factor it, '3x' and 'x'
(3x ± ?)(x ± ?)

12 has 3 ways you can factor it, 12 and 1, 6 and 2, and 3 and 4. 12 and 1 will definitely not work any way, 6 and 2 does not work, either, so the only option is 3 and 4. But which order? 3x gets the negative since its bigger. So the result is:
(3x - 4)(x + 3)

it would be:
(3x+4)(x-3)