Factor polynomial $$ 4c^{2}+9c+2 $$

$$ 4c^{2}+9c+2 = ( 4c+1 )( c+2 ) $$

Step 1: 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:

$$ a = 4 , b = 9 ~ \text{ and } ~ c = 2 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = 2} $.

$$ a \cdot c = 8 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 8 $ and add to $ b = 9 $.

Step 4: All pairs of numbers with a product of $ 8 $ are:

PRODUCT = 8
1     8	-1     -8
2     4	-2     -4

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 9 }$

PRODUCT = 8 and SUM = 9
1     8	-1     -8
2     4	-2     -4

Step 6: Replace middle term $ 9 x $ with $ 8x+x $:

$$ 4x^{2}+9x+2 = 4x^{2}+8x+x+2 $$

Step 7: Apply factoring by grouping. Factor $ 4x $ out of the first two terms and $ 1 $ out of the last two terms.

$$ 4x^{2}+8x+x+2 = 4x\left(x+2\right) + 1\left(x+2\right) = \left(4x+1\right) \left(x+2\right) $$

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