factor the basic trinomial:

Question

x^2-4x+24 trinomial

Answer 1

To factor the trinomial x^2 - 4x + 24, we first need to find two numbers that multiply to 24 and add up to -4 (the coefficient of the x term).

The two numbers that make up 24 and add up to -4 are -2 and -12.

So, we can rewrite the trinomial as:
x^2 - 4x + 24 = x^2 - 2x - 12x + 24

Now, we can factor by grouping:
= x(x - 2) - 12(x - 2)
= (x - 2)(x - 12)

Therefore, the factored form of the trinomial x^2 - 4x + 24 is (x - 2)(x - 12).