# How do you factor the expression 5x^2 - 16x + 3?

Dec 4, 2015

$\left(5 x - 1\right) \left(x - 3\right)$

#### Explanation:

Given: $5 {x}^{2} - 16 x + 3$

The 3 is a prime number so can only have {1, 3} as factors.
It is positive so the signs in the brackets are the same
The coefficient of x is negative (-16x) so they must both be negative.

The 5 is also a prime number so can only have {1, 5} as factors.

It is just a matter of getting them in the correct order

$\textcolor{b l u e}{\text{Attempt 1}}$

$\left(5 x - 3\right) \left(x - 1\right) = 5 {x}^{2} - 8 x \ldots \textcolor{red}{\text{Fail}}$

This will not work so there is no point in continuing with the rest of the multiplication.

$\textcolor{b l u e}{\text{Attempt 2}}$

$\textcolor{b l u e}{\left(5 x - 1\right) \left(x - 3\right)} \textcolor{b r o w n}{= 5 {x}^{2} - 15 x - x + 3} \textcolor{b l u e}{= 5 {x}^{2} - 16 x + 3}$