Step 1 :
After factoring out $ 3 $ we have:
$$ 3x^{2}-15x+18 = 3 ( x^{2}-5x+6 ) $$Step 2 :
Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:
$$ \color{blue}{ b = -5 } ~ \text{ and } ~ \color{red}{ c = 6 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -5 } $ and multiply to $ \color{red}{ 6 } $.
Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 6 }$.
PRODUCT = 6 | |
1 6 | -1 -6 |
2 3 | -2 -3 |
Step 4: Find out which pair sums up to $\color{blue}{ b = -5 }$
PRODUCT = 6 and SUM = -5 | |
1 6 | -1 -6 |
2 3 | -2 -3 |
Step 5: Put -2 and -3 into placeholders to get factored form.
$$ \begin{aligned} x^{2}-5x+6 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-5x+6 & = (x -2)(x -3) \end{aligned} $$