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

Question

Avery Alexander · Accepted Answer

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.

Isaiah Anthony · Answer

undefined To factor the expression $m^2 + m - 90$, you need to find two numbers that multiply to -90 and add up to +1. The numbers are +10 and -9. So, you can factor the expression as follows:

$m^2 + m - 90 = (m + 10)(m - 9)$