How do you factor #x² - x - 90#?

1 Answer
Mar 9, 2018

Answer:

#(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)#