Question

How do you factor 12x^2+8x-15? Thanks in advance.

Answer 1

Look for combinations of 4 and 3, or 6 and 2, for the x term of one monomial factor, and 5 and 3 for the constant term, and see what works
Example:

(4x -3)(3x +5) gives 12 x^2 +11 x -15
(6x -5)(2x +3) gives ?

It's a trial and error process of picking suitable factors that yield the right coefficients for the x^2 and constant terms, and seeing what the middle term coefficient of x turns out to be.

If that doesn't work, you can always go back to the equation
x = [-b +/2 sqrt(b^2-4ac)]/2a and taking the opposite sign of the roots. If the roots are m and n, the equation
ax^2 + bx + c = 0 factors to a(x-m)(x-n) = 0.

Answer 2

Couldn't you also have (12x-__)(1x+___) or (__-15)(___+3), etc? Isn't there an easier way then this guess and check process???