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).

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).

mathmate · Answer

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

mathmate · Answer

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).