Answer:
3x^2 + 20x + 12 is (3x + 2)(x + 6)
Explanation:
To factor the trinomial 3x^2 + 20x + 12, we look for two binomials in the form (ax + b)(cx + d) that multiply together to give the trinomial.
We can start by looking for factors of 3x^2, which are 3x and x. Then, we look for factors of 12, which are 1, 2, 3, 4, 6, and 12. We need to find a combination of these factors that will give us 20x when combined.
The factors of 12 are:
1, 2, 3, 4, 6, 12
We can try different combinations to see which one works:
(3x + 4)(x + 3) = 3x^2 + 9x + 4x + 12 = 3x^2 + 13x + 12
(3x + 6)(x + 2) = 3x^2 + 6x + 12x + 24 = 3x^2 + 18x + 24
(3x + 12)(x + 1) = 3x^2 + 3x + 12x + 12 = 3x^2 + 15x + 12
(3x + 2)(x + 6) = 3x^2 + 18x + 2x + 12 = 3x^2 + 20x + 12
From the combinations we tried, we see that (3x + 2)(x + 6) gives us the correct combination of factors. Therefore, the factored form of 3x^2 + 20x + 12 is (3x + 2)(x + 6).