SOLUTION: What is the coefficient of the term free of x of the expansion of (2x - 5y)^4 The degree of the polynomial f(x) whose only root is 3 of multiplicity 3 is three. TRUE or False

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the coefficient of the term free of x of the expansion of (2x - 5y)^4 The degree of the polynomial f(x) whose only root is 3 of multiplicity 3 is three. TRUE or False      Log On


   



Question 1001659: What is the coefficient of the term free of x of the expansion of (2x - 5y)^4
The degree of the polynomial f(x) whose only root is 3 of multiplicity 3 is three. TRUE or False

Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The coefficient of the term without an x is (-5y)^4.
The coefficient is (-5)^4=625.
Only root of 3 is multiplicity 3 is degree three. TRUE. If the only REAL root is 3, it is possible for the polynomial to have complex roots.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
What is the coefficient of the term free of x of the expansion of (2x - 5y)^4
The degree of the polynomial f(x) whose only root is 3 of multiplicity 3 is three. TRUE or False
An x doesn't exist at the term where x = x%5E%28n+-+n%29. This is at the 5th term of the expansion, or more specifically at: %22+%22%5B4%5DC%5B4%5D+%2A+%282x%29%5E%284+-+4%29+%2A+%28-+5y%29%5E4.
This results in: 1+%2A+%282x%29%5E0+%2A+%28-+5y%29%5E4 -------> 1+%2A+1+%2A+625y%5E4 -------> 625y%5E4, which gives a coefficient of: highlight_green%28625%29