Question

How do you factor `2a^2+3a+1`?

Answer 1

`2a^2+3a+1=2(a+1/2)(a+1)`

Explanation:

We evaluate the discriminant: `Delta=B^2-4AC=9-8=1`.
The roots are given by `a=(-B pm sqrt(Delta))/(2A)`.
Here we have `a_1=(-3+1)/4=-1/2` and `a_2=(-3-1)/4=-1`.
The factored form is `A(a-a_1)(a-a_2)=2(a+1/2)(a+1)`.