Factor polynomial $$ 15w^{2}+39w+18 $$

$$ 15w^{2}+39w+18 = 3( 5w+3 )( w+2 ) $$

Step 1 :

After factoring out $ 3 $ we have:

$$ 15w^{2}+39w+18 = 3 ( 5w^{2}+13w+6 ) $$

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:

$$ a = 5 , b = 13 ~ \text{ and } ~ c = 6 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = 6} $.

$$ a \cdot c = 30 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 30 $ and add to $ b = 13 $.

Step 5: All pairs of numbers with a product of $ 30 $ are:

PRODUCT = 30
1     30	-1     -30
2     15	-2     -15
3     10	-3     -10
5     6	-5     -6

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 13 }$

PRODUCT = 30 and SUM = 13
1     30	-1     -30
2     15	-2     -15
3     10	-3     -10
5     6	-5     -6

Step 7: Replace middle term $ 13 x $ with $ 10x+3x $:

$$ 5x^{2}+13x+6 = 5x^{2}+10x+3x+6 $$

Step 8: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ 3 $ out of the last two terms.

$$ 5x^{2}+10x+3x+6 = 5x\left(x+2\right) + 3\left(x+2\right) = \left(5x+3\right) \left(x+2\right) $$

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