Answer:
(x + 1)(2x + 1)
Step-by-step explanation:
To factor the expression 2x^2 + 3x + 1, we will find two numbers that adds up to 3 and multiplies to 2. Whenever you have a trinomial like this and need to factor, find two numbers that adds up to the middle term and multiplies to product the first term and the third term.
So the two numbers are 1 and 2. So we will replace the middle term, which is 3x with 1x and 2x. And we'll have:
2x^2 + x + 2x + 1
Now we will split this expression up:
(2x^2 + x) + (2x + 1)
We will find the greatest common factor for both expressions in the parentheses and factor:
x(2x + 1) + 1(2x + 1)
Factor:
(x + 1)(2x + 1)
