1) Find the constant c such that (x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)= 0, for all x.
2) When the expression 4(x^2-2x+2)-7(x^3-3x+1) is fully simplified, what is the sum of the squares of the coefficients of the terms?
3) 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).
The next two problems are connected.
4) 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).
5) 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) + a * g(x).
The next ones are not related to problems 4 and 5.
6) 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?
7) Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. What is the degree of f(x) * g(x).
Thank you for your time!!!
Questions 2, 3, and 7 are straight-forward questions. Have you tried these?
Question 1 can be tricky. What have you done, so far, in attempting this problem?
Question 4: What is the degree of f(x) + g(x)? Can the constant 'a' change this degree?
Question 5: What value for 'a' can change the degree of the sum?
Question 6 asks you to find the equation of a quadratic. Do you know how to do this?