Problem 1)
Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the coefficient of x^3 in the sum f(x) + g(x)?
Problem 2a)
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)?
Problem 2b)
Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b • g(x)?
+9466 Problem 1)
f(x) = x3 + 3x2 + 4x - 7
g(x) = -7x4 + 5x3 + x2 - 7
We only need to look at the x3 terms.
x3 + 5x3 = 6x3 so the coefficient of x3 in f(x) + g(x) is 6 .
Problem 2)
f(x) = x4 - 3x2 + 2
g(x) = 2x4 - 6x2 + 2x - 1
a)
The largest possible degree of f(x) + a * g(x) is just 4 .
b)
If b = -1/2 , then the x4 terms cancel and the x2 terms cancel in f(x) + b * g(x) so the degree would be 1 .
