Factor polynomial $$ -3x^{2}+45x-78 $$

$$ -3x^{2}+45x-78 = ( -3 )( x-2 )( x-13 ) $$

Step 1 :

After factoring out $ -3 $ we have:

$$ -3x^{2}+45x-78 = -3 ( x^{2}-15x+26 ) $$

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:

$$ \color{blue}{ b = -15 } ~ \text{ and } ~ \color{red}{ c = 26 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -15 } $ and multiply to $ \color{red}{ 26 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 26 }$.

PRODUCT = 26
1     26	-1     -26
2     13	-2     -13

Step 4: Find out which pair sums up to $\color{blue}{ b = -15 }$

PRODUCT = 26 and SUM = -15
1     26	-1     -26
2     13	-2     -13

Step 5: Put -2 and -13 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-15x+26 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-15x+26 & = (x -2)(x -13) \end{aligned} $$

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