How do you factor 3x^2-7x+4 by grouping?

Jan 19, 2017

$3 {x}^{2} - 7 x + 4 = \left(3 x - 4\right) \left(x - 1\right)$

Explanation:

Note that $7 = 3 + 4$, so we can split the middle term as $- 3 x - 4 x$ to be able to factor by grouping:

$3 {x}^{2} - 7 x + 4 = 3 {x}^{2} - 3 x - 4 x + 4$

$\textcolor{w h i t e}{3 {x}^{2} - 7 x + 4} = \left(3 {x}^{2} - 3 x\right) - \left(4 x - 4\right)$

$\textcolor{w h i t e}{3 {x}^{2} - 7 x + 4} = 3 x \left(x - 1\right) - 4 \left(x - 1\right)$

$\textcolor{w h i t e}{3 {x}^{2} - 7 x + 4} = \left(3 x - 4\right) \left(x - 1\right)$