factor the basic trinomial:
6x^2 - 66x + 60
To factor the trinomial 6x^2 - 66x + 60, we first look for common factors of all three terms. In this case, all terms are divisible by 6:
6x^2 - 66x + 60
= 6(x^2 - 11x + 10)
Next, we look for two numbers that multiply to the constant term (10) and add up to the coefficient of the x term (-11). These numbers are -10 and -1:
6(x - 10)(x - 1)
Therefore, the factored form of the trinomial 6x^2 - 66x + 60 is 6(x - 10)(x - 1).