If (x + 2) is a factor of m^2x^4 + 5mx^3 + x^2 – 7x – 2, find m. (4 marks)
There is no reason to keep changing names.
You have several questions all of the same nature.
The only way to learn how to do these is by doing lots yourself.
They are a simple application of the Factor Theorem.
If x+2 is a factor, then f(-2) = 0
m^2(16) + 5m(-8) + 4 - 7(-2) - 2 = 0
16m^2 - 40m + 16 = 0
2m^2 - 5m + 2 = 0
(2m - 1)(m - 2) = 0
m = 1/2 or m = 2