Homework Help: Find an annihilator of x^2 + 2x^5

1. Aug 17, 2016

magnesium12

1. The problem statement, all variables and given/known data
Find an annihilator of x2+2x5.

2. Relevant equations
xnecx -----> [D-c]n+1

[Q1(D)Q2(D)] = b1(x) + b2(x)
3. The attempt at a solution

x2 -----> D3

2x5-----> D6

x2 + 2x5 ------> (D3)(D6) = D18

Last edited by a moderator: Aug 17, 2016
2. Aug 17, 2016

Staff: Mentor

Doesn't the D6 operator also annihilate x2?

3. Aug 17, 2016

magnesium12

I guess it does. So does that mean there can be multiple annihilators and they'll all work? Or should you always pick the least common multiple?

4. Aug 17, 2016

vela

Staff Emeritus
What does the last line mean? It's not clear to me.

Why are you multiplying the two annihilators?

5. Aug 17, 2016

Staff: Mentor

Didn't notice this before -- is x3x6 = x18?

6. Aug 17, 2016

Staff: Mentor

Dn+1 annihilates xn and all lower powers of x. I don't see that this is related to the LCM in any way.

7. Aug 17, 2016

vela

Staff Emeritus
Heh...I didn't notice that either.