Factor polynomial $$ x^{2}+11x+28 $$

$$ x^{2}+11x+28 = ( x+4 )( x+7 ) $$

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:

$$ \color{blue}{ b = 11 } ~ \text{ and } ~ \color{red}{ c = 28 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 11 } $ and multiply to $ \color{red}{ 28 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 28 }$.

PRODUCT = 28
1     28	-1     -28
2     14	-2     -14
4     7	-4     -7

Step 3: Find out which pair sums up to $\color{blue}{ b = 11 }$

PRODUCT = 28 and SUM = 11
1     28	-1     -28
2     14	-2     -14
4     7	-4     -7

Step 4: Put 4 and 7 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+11x+28 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+11x+28 & = (x + 4)(x + 7) \end{aligned} $$

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