-4x² - 10x + 6
[ax² + bx + c]
Multiply the first and last number (a and c) together.
-4(6) = -24
Now find the factors of 24 that can add or subtract to -10 (b)
24 = 1, 2, 3, 4, 6, 8, 12, 24 ( 1 × 24, 2 × 12, 3 × 8, 4 × 6 )
2 and 12, and 4 and 6 can add or subtract to -10. I will be using 2 and 12.
Now instead of this:
-4x² - 10x + 6
You can replace -10x with:
-4x² + 2x - 12x + 6 (this is because the sum of 2x and -12x is -10x)
Now factor separately (factor -2x from [-4x² + 2x], and factor -6 from [-12x + 6])
-2x(2x - 1) - 6(2x - 1)
Factor (2x - 1) out
(2x - 1)(-2x - 6)