Question
which of the following are factors for the polynomial 6x^2+36x+54
a. (2x+6)(3x+3)
b.6(x+3)(x+3)
c.3(x+6)(x+3)
d.6(x+9)(x+6)
a. (2x+6)(3x+3)
b.6(x+3)(x+3)
c.3(x+6)(x+3)
d.6(x+9)(x+6)
Answers
GPT 3.5
To determine the factors of the polynomial 6x^2 + 36x + 54, we can try factoring out a common factor of 6 first.
Dividing each term by 6, we have:
(6x^2 + 36x + 54) รท 6
= x^2 + 6x + 9
Now we can try to factor this quadratic trinomial. It can be factored as (x + 3)(x + 3), which is equivalent to (x + 3)^2.
So we have: (x + 3)^2
Multiplying back by the common factor of 6, we get:
6(x + 3)^2
Therefore, the correct factorization is option b. 6(x + 3)(x + 3).
Dividing each term by 6, we have:
(6x^2 + 36x + 54) รท 6
= x^2 + 6x + 9
Now we can try to factor this quadratic trinomial. It can be factored as (x + 3)(x + 3), which is equivalent to (x + 3)^2.
So we have: (x + 3)^2
Multiplying back by the common factor of 6, we get:
6(x + 3)^2
Therefore, the correct factorization is option b. 6(x + 3)(x + 3).