Question

9x^2-38x+8
a. fins two numbers whose product is 9*8=72 and whose sum is -38.
b. write -38x using the factors from part (a).

Answer 1

Make a table of the candidates and check if they fit the criteria
A B A+B AB
-1 -72 -73 72
-2 -36 -38 72
-3 -24 -27 72
-4 -18 -22 72
-6 -12 -18 72
....
We notice that -2 and -36 fit the given requirements of sum=-38, product=72.
So
9x^2-38x+8 = 9x^2- 36x -2x +8 = 9x(x-4) - 2(x-4) = (9x-2)(x-4)
Notice that 9*4=36, 2*1=2, and -36-2=-38

Answer 2

Note: the idea is that as you do more of these exercises, the tabular part can be done mentally (that's why knowing the times table is important in math).