The given quadratic is 4x² - 5x - 6.

Possible factorizations of 4x² are 2x ^. 2x or 4x ^. x

Possible factorizations of -6 are (-3) ^. 2, 3 ^. (-2), (-6) ^. 1 or 6 ^. (-1).

We now systematically try out all the possibilities until we come up with the correct one. For instance, the choices 2x ^. 2x and (-3) ^. 2 give

(2x - 3)(2x + 2) = 4x² - 2x - 6. No good.

The choices 4x ^. x and (-3) ^. 2 give

(4x - 3)(x + 2) = 4x² + 5x - 6.

This is almost correct, except for the sign of the middle term. We can fix this by switching signs.

(4x + 3)(x - 2) = 4x² - 5x - 6

Enter this as (4*x + 3)*(x - 2)

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