Factor polynomial $$ 3x^{2}-20x+25 $$

$$ 3x^{2}-20x+25 = ( x-5 )( 3x-5 ) $$

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:

$$ a = 3 , b = -20 ~ \text{ and } ~ c = 25 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 25} $.

$$ a \cdot c = 75 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 75 $ and add to $ b = -20 $.

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 $\color{blue}{ b = -20 }$

PRODUCT = 75 and SUM = -20
1     75	-1     -75
3     25	-3     -25
5     15	-5     -15

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

$$ 3x^{2}-20x+25 = 3x^{2}-5x-15x+25 $$

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

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

Polynomial Factoring Calculator