factor the trinomial below
x^2 +15x+56
To factor the trinomial x^2 + 15x + 56, we need to find two numbers that multiply to 56 (the constant term) and add up to 15 (the coefficient of the middle term).
The two numbers that multiply to 56 and add up to 15 are 8 and 7.
Therefore, we can rewrite the trinomial as:
x^2 + 15x +56 = x^2 + 8x + 7x + 56
Now, we can factor by grouping:
x^2 + 8x + 7x + 56
x(x + 8) + 7(x + 8)
(x + 7)(x + 8)
So, the factored form of the trinomial x^2 + 15x + 56 is (x + 7)(x + 8).