# How do you factor the trinomial 2x^2-5x+3 ?

Mar 19, 2016

$\left(x - 1\right) \left(2 x - 3\right)$

#### Explanation:

Given :$2 {x}^{2} - 5 x + 3$ , this quadratic equation can be factored, if I can find two numbers which multiply together to equal $6$ and add together to equal $- 5$. I can, and they are $- 3$ and $- 2$. So now I will use them to expand the original expression.
$2 {x}^{2} - 5 x + 3$
$2 {x}^{2} - 2 x - 3 x + 3$

Notice that I have rewritten the term $- 5 x$ as the sum of $- 2 x + \left(- 3 x\right)$. Now I will do some simple factoring:

$2 x \left(x - 1\right) - 3 \left(x - 1\right)$. Notice that $\left(x - 1\right)$ is a common term, so I can factor it and get the solution.

$\left(x - 1\right) \left(2 x - 3\right)$