Final answer:
The expression 2g^2 + 13g + 11 is factored as (2g + 11)(g + 1), found through combining factors that multiply to 22 and add to 13.
Step-by-step explanation:
To factor the expression 2g^2 + 13g + 11, you need to find two numbers that multiply to give the product of the coefficient of g^2 (which is 2) and the constant term (which is 11), and at the same time, these two numbers should add up to the coefficient of the g term (which is 13).
In this case, the numbers are 2 and 11 themselves because 2 * 11 = 22 and 2 + 11 = 13. Therefore, the expression can be factored as:
(2g + 11)(g + 1)
This is done through the process often called 'trial and error' or 'factoring by grouping' where you experiment with different combinations of factors until you find the correct one that works for both conditions mentioned above.