Problems from Product of polynomials

Consider the following polynomials:

$p (x) = - x^{3} + x$

$r (x) = - x + 1$

Do the following operation: $r (x) \cdot p (x)$

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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:

$p (x) \cdot r (x) = (x^{4} - x^{3}) + (- x^{2} + x) = x^{4} - x^{3} - x^{2} + x$

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