factor each trinomial completely
x^2 + 4x - 12
x^2 + 11x + 18
To factor the trinomials completely, we need to find two numbers that multiply to the constant term and add up to the coefficient of the middle term.
1. x^2 + 4x - 12
The constant term in this trinomial is -12 and the middle term is 4. The two numbers that multiply to -12 and add up to 4 are 6 and -2. So we can rewrite the trinomial as:
x^2 + 6x - 2x - 12
Factor by grouping:
x(x + 6) - 2(x + 6)
(x - 2)(x + 6)
2. x^2 + 11x + 18
The constant term in this trinomial is 18 and the middle term is 11. The two numbers that multiply to 18 and add up to 11 are 9 and 2. So we can rewrite the trinomial as:
x^2 + 9x + 2x + 18
Factor by grouping:
x(x + 9) + 2(x + 9)
(x + 2)(x + 9)
Therefore, the factored form of each trinomial is:
1. x^2 + 4x - 12 = (x - 2)(x + 6)
2. x^2 + 11x + 18 = (x + 2)(x + 9)