Which term can be used in the blank of 36x^3-22x^- so the greatest common factor of the resulting polynomial is 2x?

144x

Step-by-step explanation:

36x^3-22x^2-144x

This is the expression which has G.C.F 2x.

We can solve it:

Find the factors of each term one by one

Factors of 36x³

36 = 2² * 3²

36 = 1,2,3,4,6,9,12,18 and 36

x³ = 1,x,x²,x³

Factors of  22x²

22 = 2*11

22 = 1,2,11,22

x² = 1, x, x²

Factors of  144x

144 = 2^4 * 3²

144 = 1,2,3,4,6,9,12,18,24,36,48,72,144

x= 1,x

Thus the G.C.F is 2x

Therefore it is now proved that 144x is the term