Answer:
(2x - 5)(3x + 1)
Explanation:
6x² - 13x - 5
you can solve this by factoring method by observing the factors of the x² term or the constant term. But because in this case the x² term is 6 (i.e ≠ 1), it will probably be easier to find the roots of the equation.
We'll use completing the square:
let 6x² - 13x - 5 = 0 (divide both sides by 6, to make the x² term = 1)
(6x² - 13x) / 6 = 5 /6
x² - (13/6)x = 5 /6 (complete the square by adding [(13/6)÷2 ]²= (13/12)² to both sides)
x² - (13/6)x + (13/12)²= 5 /6 + (13/12)²
[x - (13/12) ]² = 289/144
x - (13/12) = ±√(289/144)
x - (13/12) = ± (17/12)
x = (13/12) ± (17/12)
hence
x = (13/12) + (17/12)
x = 5/2
2x = 5
2x-5 = 0 ---> hence (2x - 5) is a factor
OR
x = (13/12) - (17/12)
x = -1/3
3x = -1
3x+1 = 0 ---> hence (3x + 1) is a factor
Since we know that a quadratic equation can have at most 2 real roots, we can conclude that these are the only 2 real factors
Combining the 2 factors we have found,
6x² - 13x - 5 = (2x - 5)(3x + 1)