Factor polynomial $$ 4x^{2}+6x-4048 $$

$$ 4x^{2}+6x-4048 = 2( 2x^{2}+3x-2024 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 4x^{2}+6x-4048 = 2 ( 2x^{2}+3x-2024 ) $$

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:

$$ a = 2 , b = 3 ~ \text{ and } ~ c = -2024 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -2024} $.

$$ a \cdot c = -4048 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -4048 $ and add to $ b = 3 $.

Step 5: All pairs of numbers with a product of $ -4048 $ are:

PRODUCT = -4048
-1     4048	1     -4048
-2     2024	2     -2024
-4     1012	4     -1012
-8     506	8     -506
-11     368	11     -368
-16     253	16     -253
-22     184	22     -184
-23     176	23     -176
-44     92	44     -92
-46     88	46     -88

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 3 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 3 }$, we conclude the polynomial cannot be factored.

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