factor the polynomial 3h^2+11h+6

Factor the 6. Which factor times 3 plus the other factor = 11?

To factor the polynomial 3h^2 + 11h + 6, we need to find two numbers whose product is 3 * 6 = 18 and whose sum is 11.

Let's think about the numbers that have a product of 18: 1 * 18, 2 * 9, or 3 * 6.
Now, we need to check if any of these pairs of numbers also add up to 11.
By looking at the pairs, we can see that 3 * 6 = 18 and 3 + 6 = 9 (not 11).
Let's try another pair: 2 * 9 = 18 and 2 + 9 = 11.
So, we have found our two numbers: 2 and 9.
Now, we can rewrite the polynomial as follows:
3h^2 + 11h + 6 = 3h^2 + 2h + 9h + 6.
Next, we group the terms and factor by grouping:
(3h^2 + 2h) + (9h + 6)
Now, let's factor from each group:
h(3h + 2) + 3(3h + 2)
As we can see, both groups have a common factor of (3h + 2):
(3h + 2)(h + 3)
Therefore, the factored form of the polynomial 3h^2 + 11h + 6 is (3h + 2)(h + 3).