Factor polynomial $$ 4x^{2}+15x-25 $$

$$ 4x^{2}+15x-25 = ( 4x-5 )( x+5 ) $$

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:

$$ a = 4 , b = 15 ~ \text{ and } ~ c = -25 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = -25} $.

$$ a \cdot c = -100 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -100 $ and add to $ b = 15 $.

Step 4: All pairs of numbers with a product of $ -100 $ are:

PRODUCT = -100
-1     100	1     -100
-2     50	2     -50
-4     25	4     -25
-5     20	5     -20
-10     10	10     -10

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 15 }$

PRODUCT = -100 and SUM = 15
-1     100	1     -100
-2     50	2     -50
-4     25	4     -25
-5     20	5     -20
-10     10	10     -10

Step 6: Replace middle term $ 15 x $ with $ 20x-5x $:

$$ 4x^{2}+15x-25 = 4x^{2}+20x-5x-25 $$

Step 7: Apply factoring by grouping. Factor $ 4x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 4x^{2}+20x-5x-25 = 4x\left(x+5\right) -5\left(x+5\right) = \left(4x-5\right) \left(x+5\right) $$

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