Factor polynomial $$ 15s^{2}+50s+15 $$

$$ 15s^{2}+50s+15 = 5( 3s+1 )( s+3 ) $$

Step 1 :

After factoring out $ 5 $ we have:

$$ 15s^{2}+50s+15 = 5 ( 3s^{2}+10s+3 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 3 , b = 10 ~ \text{ and } ~ c = 3 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 9 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 9 $ and add to $ b = 10 $.

Step 5: All pairs of numbers with a product of $ 9 $ are:

PRODUCT = 9
1     9	-1     -9
3     3	-3     -3

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 10 }$

PRODUCT = 9 and SUM = 10
1     9	-1     -9
3     3	-3     -3

Step 7: Replace middle term $ 10 x $ with $ 9x+x $:

$$ 3x^{2}+10x+3 = 3x^{2}+9x+x+3 $$

Step 8: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ 1 $ out of the last two terms.

$$ 3x^{2}+9x+x+3 = 3x\left(x+3\right) + 1\left(x+3\right) = \left(3x+1\right) \left(x+3\right) $$

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