Question

How do you factor `9x^2 - 36x + 24`?

Answer 1

9(x - x1)(x - x2)

Explanation:

`f(x) = 3y = 3(3x^2 - 12x + 8)`
Factor y, the trinomial in parentheses -->
`y = 3x^2 - 12x + 8`
`D = b^2 - 4ac = 144 - 96 = 48` --> `d = +-4sqrt3`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = 2 +- (2sqrt3)/3`
The 2 real roots are:
`x1 = 2 + (2sqrt3)/3`
`x2 = 2 - (2sqrt3)/3`
f(x) can be written in the factored form:

#f(x) = 3y = 9(x - x1)(x - x2) = = 9(x - 2 + (2sqrt3)/3)(x - 2 - (sqrt3)/3)#