Factor polynomial $$ 5m^{2}+22m-15 $$

$$ 5m^{2}+22m-15 = ( 5m-3 )( m+5 ) $$

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:

$$ a = 5 , b = 22 ~ \text{ and } ~ c = -15 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -15} $.

$$ a \cdot c = -75 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -75 $ and add to $ b = 22 $.

Step 4: All pairs of numbers with a product of $ -75 $ are:

PRODUCT = -75
-1     75	1     -75
-3     25	3     -25
-5     15	5     -15

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 22 }$

PRODUCT = -75 and SUM = 22
-1     75	1     -75
-3     25	3     -25
-5     15	5     -15

Step 6: Replace middle term $ 22 x $ with $ 25x-3x $:

$$ 5x^{2}+22x-15 = 5x^{2}+25x-3x-15 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -3 $ out of the last two terms.

$$ 5x^{2}+25x-3x-15 = 5x\left(x+5\right) -3\left(x+5\right) = \left(5x-3\right) \left(x+5\right) $$

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