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:

$$ a = 9 , b = -97 ~ \text{ and } ~ c = 144 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 144} $.

$$ a \cdot c = 1296 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 1296 $ and add to $ b = -97 $.

Step 4: All pairs of numbers with a product of $ 1296 $ are:

PRODUCT = 1296
1     1296	-1     -1296
2     648	-2     -648
3     432	-3     -432
4     324	-4     -324
6     216	-6     -216
8     162	-8     -162
9     144	-9     -144
12     108	-12     -108
16     81	-16     -81
18     72	-18     -72
24     54	-24     -54
27     48	-27     -48
36     36	-36     -36

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -97 }$

PRODUCT = 1296 and SUM = -97
1     1296	-1     -1296
2     648	-2     -648
3     432	-3     -432
4     324	-4     -324
6     216	-6     -216
8     162	-8     -162
9     144	-9     -144
12     108	-12     -108
16     81	-16     -81
18     72	-18     -72
24     54	-24     -54
27     48	-27     -48
36     36	-36     -36

Step 6: Replace middle term $ -97 x $ with $ -16x-81x $:

$$ 9x^{2}-97x+144 = 9x^{2}-16x-81x+144 $$

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

$$ 9x^{2}-16x-81x+144 = x\left(9x-16\right) -9\left(9x-16\right) = \left(x-9\right) \left(9x-16\right) $$

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