Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of \(f(x) + a\cdot g(x)?\)

TheEarlyMathster Apr 30, 2021

#4**+1 **

Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of f(x) + a(g(x))?

Since we are told that a is a constant, and since the coefficient does not matter so a doesn’t matter. We just need to find the degree of f(x), add it by the degree of g(x) [this is because for any a, b, c, d, a^b * c^d = ac ^ (b+d)] . The degree of f(x) is 4 and the degree of g(x) is 4. We found that the degree are both the same, and it is not multiply (which I thought before) so the largest degree is 4.

MathProblemSolver101 Apr 30, 2021