Factor polynomial $$ -5x^{2}+45x-90 $$

$$ -5x^{2}+45x-90 = ( -5 )( x-3 )( x-6 ) $$

Step 1 :

After factoring out $ -5 $ we have:

$$ -5x^{2}+45x-90 = -5 ( x^{2}-9x+18 ) $$

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:

$$ \color{blue}{ b = -9 } ~ \text{ and } ~ \color{red}{ c = 18 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -9 } $ and multiply to $ \color{red}{ 18 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 18 }$.

PRODUCT = 18
1     18	-1     -18
2     9	-2     -9
3     6	-3     -6

Step 4: Find out which pair sums up to $\color{blue}{ b = -9 }$

PRODUCT = 18 and SUM = -9
1     18	-1     -18
2     9	-2     -9
3     6	-3     -6

Step 5: Put -3 and -6 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-9x+18 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-9x+18 & = (x -3)(x -6) \end{aligned} $$

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