Consider the following polynomials:
$$p(x)=-x^3+x$$
$$q(x)=2x^3-x-3$$
Do the following operation: $$p(x)+q(x)$$
See development and solution
Development:
| p(x) | q(x) | p(x)+q(x) | |
| degree 0 | $$0$$ | $$-3$$ | $$-3$$ |
| degree 1 | $$x$$ | $$-x$$ | $$0$$ |
| degree 2 | $$0$$ | $$0$$ | $$0$$ |
| degree 3 | $$-x^3$$ | $$2x^3$$ | $$x^3$$ |
Solution:
$$p(x)+q(x)=x^3-3$$