Consider the following polynomials:
$$p(x)=-x^3+x$$
$$r(x)=-x+1$$
Do the following operation: $$r(x)\cdot p(x)$$
See development and solution
Development:
Calculate the product of $$r(x)$$ by the monomials of $$p(x)$$: $$$(-x^3)\cdot r(x)=-x^3\cdot(-x+1)=+x^4-x^3$$$ $$$x\cdot r(x)=x\cdot(-x+1)=-x^2+x$$$
Solution:
We put together both polynomials and we make groups of similar terms:
$$p(x)\cdot r(x)=(x^4-x^3)+(-x^2+x)=x^4-x^3-x^2+x$$