Factor polynomial $$ 14w^{2}+20w+6 $$

$$ 14w^{2}+20w+6 = 2( 7w+3 )( w+1 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 14w^{2}+20w+6 = 2 ( 7w^{2}+10w+3 ) $$

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:

$$ a = 7 , b = 10 ~ \text{ and } ~ c = 3 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 21 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 21 $ and add to $ b = 10 $.

Step 5: All pairs of numbers with a product of $ 21 $ are:

PRODUCT = 21
1     21	-1     -21
3     7	-3     -7

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

PRODUCT = 21 and SUM = 10
1     21	-1     -21
3     7	-3     -7

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

$$ 7x^{2}+10x+3 = 7x^{2}+7x+3x+3 $$

Step 8: Apply factoring by grouping. Factor $ 7x $ out of the first two terms and $ 3 $ out of the last two terms.

$$ 7x^{2}+7x+3x+3 = 7x\left(x+1\right) + 3\left(x+1\right) = \left(7x+3\right) \left(x+1\right) $$

Polynomial Factoring Calculator