Question

how to factor the quadratic :12x^2+11x-12?

Answer 1

The given expression 12x^2 + 11x - 12 isn't "readily factorable". What I mean is that the factors of the constant c here are not integers or whole numbers in which when added gives an 11, so it's hard to factor it by one look (I hope that's clear?). So we use the quadratic formula.

For a quadratic equation in the general form, ax^2 + bx + c = 0, the quadratic formula is given by:
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a
In the given expression, 12x^2 + 11x - 12,
a = 12
b = 11
c = -12
Substituting,
x = ( -11 +/- sqrt(11^2 - 4(12)(-12)) ) / 2(12)
x = ( -11 +/- sqrt(697) ) / 24
x = ( -11 +/- 26.40076 ) / 24
x = 0.6417 (positive)
x = -1.5584 (negative)
These are the roots (if it was an equation). If we want to factor it in this format (x-m)(x-n) you'll have
12(x - 0.6417)(x + 1.5584)

hope this helps? `u`