How do you factor by grouping 10x^3+20x^2+x+2?

Apr 11, 2015

We can factorise the following expression by making groups of 2

$\left(10 {x}^{3} + 20 {x}^{2}\right) + \left(x + 2\right)$

In the first group, $10 {x}^{2}$ is common to both the terms, and in the second, $1$ is the only factor common to both the terms.

So we write the expression as

$\left(10 {x}^{2}\right) \left(x + 2\right) + 1 \cdot \left(x + 2\right)$

= color(green)((x+2)(10x^2+1)

As $10 {x}^{2} + 1$ cannot be factorised further, the above will be the factorised form of the expression $10 {x}^{3} + 20 {x}^{2} + x + 2$