# Question #7e5f1

Dec 2, 2017

$\left(u - 2\right) \left(u - 3\right)$

#### Explanation:

So basically, to factor equations in the shape of ${x}^{2} - b x + C$, we can use the method of inspection (one of the many ways to factor).

For inspection to work, we need to find two integers which have a product (multiplication) equal to c and a sum (addition) equal to b. If no two such integers exist, then the polynomial cannot be factored.

So let’s factor ${u}^{2} - 5 u + 6$

We need two integers which gives us a product equal to 6 and a sum equal to -5.

-2 and -3 are two integers, proof:

$- 2 \cdot - 3 = 6$

$\left(- 2\right) + \left(- 3\right) = - 5$

Knowing these numbers, we can find the factored form, which is $\left(u - 2\right) \left(u - 3\right)$