# How do you factor 4x^3-2x^2+6x-3?

$\left(2 x - 1\right) \left(2 {x}^{2} + 3\right)$
First, we group the terms like this: $\left(4 {x}^{3} - 2 {x}^{2}\right) + \left(6 x - 3\right)$. We can factor these groups individually: $2 {x}^{2} \left(2 x - 1\right) + 3 \left(2 x - 1\right)$.
Notice that there is a common factor: $\left(2 x - 1\right)$. We can factor this out again: $\left(2 x - 1\right) \left(2 {x}^{2} + 3\right)$. Now, we can't really factor this further. So, our answer is $\left(2 x - 1\right) \left(2 {x}^{2} + 3\right)$.