factor the basic trinomial:

Question

x^2 - 3x - 54

Answer 1

To factor the trinomial x^2 - 3x - 54, we need to find two numbers that multiply to -54 and add up to -3.

The two numbers are -9 and 6 because (-9)*(6) = -54 and (-9) + 6 = -3.

Therefore, we can rewrite the trinomial as:

x^2 - 9x + 6x - 54

Now, we can factor by grouping:
x(x - 9) + 6(x - 9)
(x + 6)(x - 9)

So, the factored form of x^2 - 3x - 54 is (x + 6)(x - 9).