Step 1 :

After factoring out $ x $ we have:

$$ 2x^{3}+9x^{2}+7x = x ( 2x^{2}+9x+7 ) $$

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:

$$ a = 2 , b = 9 ~ \text{ and } ~ c = 7 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = 7} $.

$$ a \cdot c = 14 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 14 $ and add to $ b = 9 $.

Step 5: All pairs of numbers with a product of $ 14 $ are:

PRODUCT = 14
1     14	-1     -14
2     7	-2     -7

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 9 }$

PRODUCT = 14 and SUM = 9
1     14	-1     -14
2     7	-2     -7

Step 7: Replace middle term $ 9 x $ with $ 7x+2x $:

$$ 2x^{2}+9x+7 = 2x^{2}+7x+2x+7 $$

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

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

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