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

Aug 13, 2015

color(blue)((2x-3)(x-1) is the factorised form of the expression.

#### Explanation:

$2 {x}^{2} - 5 x + 3$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot 3 = 6$
and
${N}_{1} + {N}_{2} = b = - 5$

After trying out a few numbers we get ${N}_{1} = - 2$ and ${N}_{2} = - 3$
$\left(- 2\right) \cdot \left(- 3\right) = 6$, and $\left(- 2\right) + \left(- 3\right) = - 5$

$2 {x}^{2} \textcolor{b l u e}{- 5 x} + 3 = 2 {x}^{2} \textcolor{b l u e}{- 2 x - 3 x} + 3$

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

color(blue)((2x-3)(x-1) is the factorised form of the expression.

Aug 14, 2015

factor: $y = 2 {x}^{2} - 5 x + 3$

Ans: (x - 1)(2x - 3)

#### Explanation:

Since a + b + c = 0, use the shortcut. One factor is (x - 1) and the other is $\left(x - \frac{c}{a}\right) = \left(x - \frac{3}{2}\right)$
Factoring form: y = (x - 1)( 2x - 3)
The shortcut avoids the lengthy factoring by grouping.