Factor polynomial $$ x^{2}+14x+45 $$

$$ x^{2}+14x+45 = ( x+5 )( x+9 ) $$

Step 1: 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:

$$ \color{blue}{ b = 14 } ~ \text{ and } ~ \color{red}{ c = 45 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 14 } $ and multiply to $ \color{red}{ 45 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 45 }$.

PRODUCT = 45
1     45	-1     -45
3     15	-3     -15
5     9	-5     -9

Step 3: Find out which pair sums up to $\color{blue}{ b = 14 }$

PRODUCT = 45 and SUM = 14
1     45	-1     -45
3     15	-3     -15
5     9	-5     -9

Step 4: Put 5 and 9 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+14x+45 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+14x+45 & = (x + 5)(x + 9) \end{aligned} $$

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