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 satisfy these conditions are 8 and 7, because 8 * 7 = 56 and 8 + 7 = 15.
Now, we can rewrite the trinomial as:
x^2 + 15x + 56
x^2 + 8x + 7x + 56
Now, we can factor by grouping:
x(x + 8) + 7(x + 8)
Now, we can factor out the common factor of (x + 8) from both terms:
(x + 8)(x + 7)
Therefore, the factored form of the trinomial x^2 + 15x + 56 is (x + 8)(x + 7).