Factor polynomial $$ x^{2}+95x+450 $$

$$ x^{2}+95x+450 = ( x+5 )( x+90 ) $$

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:

$$ \color{blue}{ b = 95 } ~ \text{ and } ~ \color{red}{ c = 450 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 95 } $ and multiply to $ \color{red}{ 450 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 450 }$.

PRODUCT = 450
1     450	-1     -450
2     225	-2     -225
3     150	-3     -150
5     90	-5     -90
6     75	-6     -75
9     50	-9     -50
10     45	-10     -45
15     30	-15     -30
18     25	-18     -25

Step 3: Find out which pair sums up to $\color{blue}{ b = 95 }$

PRODUCT = 450 and SUM = 95
1     450	-1     -450
2     225	-2     -225
3     150	-3     -150
5     90	-5     -90
6     75	-6     -75
9     50	-9     -50
10     45	-10     -45
15     30	-15     -30
18     25	-18     -25

Step 4: Put 5 and 90 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+95x+450 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+95x+450 & = (x + 5)(x + 90) \end{aligned} $$

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