We are looking for a factorization like
6x² + 7x - 5 = (_x + _)(_x - _)
where we need to fill in the numbers in the blanks. Since the first and third blanks multiply to 6, they have to be 1 and 6 or 2 and 3. Similarly, the second and fourth blanks multiply to 5 so they must be 1 and 5. By trial and error, we arrive at the factorization
6x² + 7x - 5 = (2x - 1)(3x + 5).
(6x - 1)(6x - 1)
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: -2 plus or minus i times the square root of 17.x = -2 + 4.123105625617661ix = -2 - 4.123105625617661iwhere i is the square root of negative one.
(3x - 4)(2x^2 + 6x + 5)
With great difficulty not knowing if 6x and 27 are plus or minus
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: -3 plus or minus i, where i is the square root of negative 1.
That factors to (x - 5)(x - 1)
x-8
(6x - 1)(6x - 1)
8x2 + 6x - 9 = 8x2 + 12x - 6x - 9 = 4x(2x + 3) - 3(2x + 3) = (2x + 3)(4x - 3)
The factors are -1(2x + 1)(3x + 4)
6x^2 -13x+6 = (3x-2)(2x-3) when factorized
(4x - 3)(2x + 3)
{-1,7}
When factored it is: (6x-1)(6x+1)
(x - 4)(x - 2)
-116
x2 - 6x - 27 = (x-9)(x+3)