Factor polynomial $$ 18b^{2}+30b-42 $$

$$ 18b^{2}+30b-42 = 6( 3b^{2}+5b-7 ) $$

Step 1 :

After factoring out $ 6 $ we have:

$$ 18b^{2}+30b-42 = 6 ( 3b^{2}+5b-7 ) $$

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:

$$ a = 3 , b = 5 ~ \text{ and } ~ c = -7 $$

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

$$ a \cdot c = -21 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -21 $ and add to $ b = 5 $.

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 $\color{blue}{ b = 5 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 5 }$, we conclude the polynomial cannot be factored.

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