Question

Factor the Trinomial:2a^2 + 3a + 1

Answer 1

2a^2 + 3a + 1

= 2a^2 + 2a + a + 1

= 2a(a + 1) + 1 (a + 1)          ( a + 1) is common)) so it is

= (2a + 1)(a + 1)  (answer)

Answer 2

Try "factoring by grouping."

The binomial factors of  2a^2 + 3a + 1  must start with a and 2a respectively, so that the product of these first terms is 2a^2.   Also note that a and 2a must add up to 3a.  They do.

Then  2a^2 + 3a + 1  = (2a+1)(a+1).