Question 477325
Please try not to write too many problems into one post; tutors are less likely to answer all of them. I'll get you started on them, but you can finish the rest.


1. (x^4 - 3x^2 + 2)(2x^4 - 6x^2 + 2x - 1) = 2x^8 + stuff. What is the degree? For parts b) and c) note that multiplying a polynomial by a constant does not change the degree. But you are adding a*g(x) to some other polynomial of the same degree, in which there exists a constant a such that the highest exponent terms cancel...


2. This one, you will have to expand, collect all the x^2 terms, and set the coefficient equal to 0. It should be some expression in terms of t, equals zero, solve for t.


3. You know f(3) = 4, but nothing else. How else would you locate a definitive point unless you set the argument of the function equal to 3?


4. The operation is commutative if a & b = b & a, and associative if (a & b)& c = a & (b & c). c) S is an identity element of & if a & S = a for all a, i.e. a + aS + S = a. d) z is the inverse if 3 & z = S, where S is the identity element. You will have solved for S from part c), so set 3 & z equal to S and solve.