Question

How do you factor `x² - x - 90`?

Answer 1

`(x-10)(x+9)`

Explanation:

To factor an expression in the form `ax^2 + bx + c`, find two numbers that multiply to get c and add to get b. For the expression `(x^2-x-90)`, the factors of -90 are `+-1, +-2, +-3, +-5, +-6, +-9, +-10, +-15, +-18, +-30, +-45, and +-90` (Note: `+-2` means "plus or minus 2" or 2 and -2).
The only two factors that multiply to -90 and add to -1 are 9 and -10.
Thus, the factors of `(x^2-x-90)` are `(x-10)` and `(x+9)` or `(x-10)(x+9)`