How do you factor 2x^2 -7x +3?

Nov 8, 2015

$2 {x}^{2} - 7 x + 3 = \left(2 x - 1\right) \left(x - 3\right)$

Explanation:

$2 {x}^{2} - 7 x + 3$ is a quadratic equation, $a {x}^{2} + b x + c$, where $a = 2 , b = - 7 , \mathmr{and} c = 3$.

Use the $a \cdot c$ method to factor this equation (also called splitting the middle).

Multiply $a$ times $c$.

$2 \times 3 = 6$

Determine two numbers that when added equal $- 7$ and when multiplied equal $6$. The numbers $- x$ and $- 6$ fit the criteria.

Rewrite the equation substituting $- x$ and $- 6 x$ for $- 7 x$.

$2 {x}^{2} - x - 6 x + 3 =$

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

Factor out the common term $\left(2 x - 1\right)$

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