factor the basic trinomial:
x^2 + 10x - 39
To factor the trinomial x^2 + 10x - 39, we need to find two numbers that multiply to -39 and add up to 10.
The two numbers that multiply to -39 and add up to 10 are 13 and -3.
Therefore, we can rewrite the trinomial as:
x^2 + 13x - 3x - 39
Now, we can factor by grouping:
x(x + 13) - 3(x + 13)
Now, we can factor out the common factor of (x + 13):
(x + 13)(x - 3)
Therefore, the factored form of the trinomial x^2 + 10x - 39 is (x + 13)(x - 3).