Assignment:
Q1) Find the quotient, q(x) , and remainder, r(x) , when x^6-2x^5+4x^3-x+1 is divided by x+1.
a) q(x)=x^5-3x^4+3x^3+x^2-x, and r(x)=1
b) q(x)=x^5-x^4-x^3+3x^2+3x-2, and r(x)=-1
c) q(x)=x^5-3x^4+7x^3-8x^2+9, and r(x)=1
d) q(x)=x^5-x^4+3x^3+2x^2+3,and r(x)=-1
Q2) How do the zeros of g(x)=4x^4-2x^3+3x^2-4x-12 compare to the zeros of f(x)=x^4-1/2x^3+3/4x^2-x-3?
a) The zeros of g(x) are 4 times the zeros of f(x).
b) The zeros of g(x) are 1/4 of the zeros of f(x).
c) Cannot be determined
d) They are the same.
Q3) Solve the polynomial equation x^3-5x^2+3x-15=0 given that x=5 is one solution.
The SUM of all the real solutions is_______
Q4) Solve: x^3-1/2x^2+4/3=11/3x^2-2/3x+4/3
The smallest zero is ________
The largest zero is _________
Provide complete and step by step solution for the question and show calculations and use formulas.