+24 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)?
2. 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)?
3. Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?
+128475 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)?
As long as "a" isn't -1/2, the largest possible degree for f(x) + a* g(x) is the fourth degree
2. 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)?
If "b" = -1/2, then the smallest possible degree for f(x) + b* g(x) is one
3. Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?
If f(0) = 47 .....then the constant term of the polynomial must be 47
And if f(1) = 32....this will equal the sum of all the coeficients.....and the sum of the coefficients on the non-constant terms of the polynomial must be - 15 because -15 + 47 = 32
