factor the basic trinomial:

Question

x^2 - x - 90

Answer 1

To factor the basic trinomial x^2 - x - 90, we need to find two numbers that multiply to -90 and add up to -1 (the coefficient in front of the x term).

The two numbers are -10 and 9, because -10 * 9 = -90 and -10 + 9 = -1.

So, we can rewrite the trinomial as:

x^2 - 10x + 9x - 90

Now, we can factor by grouping:

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

Now, we can factor out the common binomial factor x - 10:

(x - 10)(x + 9)

Therefore, the factored form of the trinomial x^2 - x - 90 is (x - 10)(x + 9).