Factor polynomial $$ 5n^{2}-47n+18 $$

$$ 5n^{2}-47n+18 = ( n-9 )( 5n-2 ) $$

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:

$$ a = 5 , b = -47 ~ \text{ and } ~ c = 18 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = 18} $.

$$ a \cdot c = 90 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 90 $ and add to $ b = -47 $.

Step 4: All pairs of numbers with a product of $ 90 $ are:

PRODUCT = 90
1     90	-1     -90
2     45	-2     -45
3     30	-3     -30
5     18	-5     -18
6     15	-6     -15
9     10	-9     -10

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -47 }$

PRODUCT = 90 and SUM = -47
1     90	-1     -90
2     45	-2     -45
3     30	-3     -30
5     18	-5     -18
6     15	-6     -15
9     10	-9     -10

Step 6: Replace middle term $ -47 x $ with $ -2x-45x $:

$$ 5x^{2}-47x+18 = 5x^{2}-2x-45x+18 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 5x^{2}-2x-45x+18 = x\left(5x-2\right) -9\left(5x-2\right) = \left(x-9\right) \left(5x-2\right) $$

Polynomial Factoring Calculator