Factor polynomial $$ 9x^{2}-89x+136 $$

$$ 9x^{2}-89x+136 = ( x-8 )( 9x-17 ) $$

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:

$$ a = 9 , b = -89 ~ \text{ and } ~ c = 136 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 136} $.

$$ a \cdot c = 1224 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 1224 $ and add to $ b = -89 $.

Step 4: All pairs of numbers with a product of $ 1224 $ are:

PRODUCT = 1224
1     1224	-1     -1224
2     612	-2     -612
3     408	-3     -408
4     306	-4     -306
6     204	-6     -204
8     153	-8     -153
9     136	-9     -136
12     102	-12     -102
17     72	-17     -72
18     68	-18     -68
24     51	-24     -51
34     36	-34     -36

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -89 }$

PRODUCT = 1224 and SUM = -89
1     1224	-1     -1224
2     612	-2     -612
3     408	-3     -408
4     306	-4     -306
6     204	-6     -204
8     153	-8     -153
9     136	-9     -136
12     102	-12     -102
17     72	-17     -72
18     68	-18     -68
24     51	-24     -51
34     36	-34     -36

Step 6: Replace middle term $ -89 x $ with $ -17x-72x $:

$$ 9x^{2}-89x+136 = 9x^{2}-17x-72x+136 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -8 $ out of the last two terms.

$$ 9x^{2}-17x-72x+136 = x\left(9x-17\right) -8\left(9x-17\right) = \left(x-8\right) \left(9x-17\right) $$

Polynomial Factoring Calculator