How do you factor 4x^2-10x+6?

Jun 15, 2018

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

Explanation:

First factor out the GCF by the distributive property:

$4 {x}^{2} - 10 x + 6$

$2 \left(2 {x}^{2} - 5 x + 3\right)$

Now the factors have to have a sum $- 5$ and a product $2 \cdot 3 = 6$

-2, -3 will work

Now factor by grouping, replace the $- 5 x$ with $- 2 x - 3 x$

$2 \left(2 {x}^{2} - 5 x + 3\right)$

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

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

now factor out $\left(x - 1\right)$

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