Question

How do you factor `m^2+m-90`?

Answer 1

f(x) = m^2 + m - 90 = (x - p)(x - q).

Find 2 numbers p and q knowing product (-90) and sum (1). Compose factor pairs of (-90). Proceed: ...(-5, 18)(-9, 10). This sum is 1 = b. Then p = -9 and q = 10.

Factored form: f(x) = (x - 9)(x + 10)

Reminder about The Rule Of Signs.

a. When a and c have different signs, compose factor pairs of c, or (a.c), with all first numbers being negative.
Example. Compose factor pairs of (-90).
Proceed: (-1, 90)(-2, 45)(-3, 30)....(-9, 10).

b. When a and c have same sign, compose factor pairs of c, or (a.c), with all positive numbers.
Example. f(x) = x^2 - 19x + 90 = 0
Proceed: (1, 90)(2, 45)....(9, 10). This last sum is (9 + 10 = 19 = -b). Then the 2 real roots are 9 and 10.