Question

How do you factor `2x^2 + 3x -12`?

Answer 1

2(x - x1)(x - x2)

Explanation:

y = 2x^2 + 3x - 12
Factored form of y:
y = a(x - x1)(x - x2)
Find x1 and x2, the 2 real roots of y. Use the improved quadratic formula.
`D = d^2 = b^2 - 4ac = 9 + 96 = 105` --> `d = +- sqrt105`
`x = -b/(2a) +- d/(2a) = -3/4 +- sqrt105/4`
Therefor,
`y = 2(x + 3/4 + sqrt105/4)(x + 3/4 - sqrt105/4)`