Question

Please help! Suppose that Q ( x ) is a quadratic polynomial. Determine the degree of the composition Q o Q(x) . Express the leading coefficient and constant terms of this composition in terms of the coefficients of Q .

Answer 1

What part of this is giving you trouble?

Answer 2

I've got Q(Q(x))= a(ax^2+bx+c)^2+b(ax^2+bx+c)+c

Answer 3

OK. That is the way to start.

Answer 4

What happens when you multiply that all out and combind like terms?

Answer 5

a^3x^4+2ba^2x^3+ab^2x^2+2ca^2x^2+abx^2+2abcx+xb^2+ac^2+bc+c

Answer 6

Yes, really long and ugly. From that you should be able to easily ee the degree, and the "leading coefficient and constant terms of this composition in terms of the coefficients of Q" are right there, at the start and end.

Answer 7

For Ax^2+Bx+C, the leading coefficient s A becayse it is what goes with the leading term. The constant is C because it has no variable. Same rules apply to your longer result.

Answer 8

So, the leading coefficient would be a^3x^4?

Answer 9

x^4 is a varriable. a^3 is a coefficent.

Answer 10

So, the leading coefficient would be a^3 and the constant would be c?

Answer 11

Yep. And what was the degree? Since they ask that.

Answer 12

4?

Answer 13

Yes! Because it is x^4 it is the 4th degree.

Answer 14

And that is all they are asking for?

Answer 15

Yah, those three items. That is it. You did not reallt even need to multiply out the whole thing, just the leading term and realize what would happen..

Actually, one correction! b is a constant, so bc is a constant! IOops, almost missed that!

So the new constant would be bc+c!!!

Answer 16

So 4th degree, a^3, bc+c