Factor polynomial $$ -5x^{2}-14x+3 $$

$$ -5x^{2}-14x+3 = -( 5x-1 )( x+3 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -5x^{2}-14x+3 = - ~ ( 5x^{2}+14x-3 ) $$

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:

$$ a = 5 , b = 14 ~ \text{ and } ~ c = -3 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -3} $.

$$ a \cdot c = -15 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -15 $ and add to $ b = 14 $.

Step 5: All pairs of numbers with a product of $ -15 $ are:

PRODUCT = -15
-1     15	1     -15
-3     5	3     -5

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 14 }$

PRODUCT = -15 and SUM = 14
-1     15	1     -15
-3     5	3     -5

Step 7: Replace middle term $ 14 x $ with $ 15x-x $:

$$ 5x^{2}+14x-3 = 5x^{2}+15x-x-3 $$

Step 8: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -1 $ out of the last two terms.

$$ 5x^{2}+15x-x-3 = 5x\left(x+3\right) -1\left(x+3\right) = \left(5x-1\right) \left(x+3\right) $$

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