# How do you factor 2x^2 + 21x + 10?

Mar 3, 2017

$\left(2 x + 1\right) \left(x + 10\right)$

#### Explanation:

To factorise $2 {x}^{2} + 21 x + 10$ we need to find two integers $p$ and $q$ such that:

$\left(2 x + p\right) \left(x + q\right) \equiv 2 {x}^{2} + 21 x + 10$

$2 {x}^{2} + \left(p + 2 q\right) x + p q \equiv 2 {x}^{2} + 21 x + 10$

$\therefore p \times q = 10$ and $2 q + p = 21$

Considering factors of 10: $1 \times 10 , 2 \times 5$

By inspection we see that $p = 1$ and $q = 10$ satisfy the conditions.

Hence: $2 {x}^{2} + 21 x + 10 = \left(2 x + 1\right) \left(x + 10\right)$

Please note: After some practice, for simple quadratic functions that can be expressed as two linear factors, as in this example, you should be able to factorise the the function by inspection - without the need to express the logic above in written form. However, you will still perform the equivalent logic mentally.