Long Division to Divide Polynomials Practice

1. Let $a(x)=5x^3-6x^2-8x+9$, and $b(x)=x^4+2x^3+x+1$.

   When dividing $a$ by $b$, we can find the unique quotient polynomial $q$ and remainder polynomial $r$ that satisfy the following equation:

   $\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$,

   where the degree of $r(x)$ is less than the degree of $b(x)$.
   What is the quotient, $q(x)$?

   $q(x)=$
   

   What is the remainder, $r(x)$? 

   $r(x)=$ 

2. Let $a(x)=-5x^3-x^2+3$, and $b(x)=x^2+4$.

   When dividing $a$ by $b$, we can find the unique quotient polynomial $q$ and remainder polynomial $r$ that satisfy the following equation:

   $\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$,

   where the degree of $r(x)$ is less than the degree of $b(x)$.
   

   What is the quotient, $q(x)$?

   $q(x)=$
   

   What is the remainder, $r(x)$?

   $r(x)=$ 

3. Let $a(x)=-12x^5-2x^3-9x$, and $b(x)=3x^4+x^2+1$.

   When dividing $a$ by $b$, we can find the unique quotient polynomial $q$ and remainder polynomial $r$ that satisfy the following equation:

   $\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$,
   

   where the degree of $r(x)$ is less than the degree of $b(x)$.
   

   What is the quotient, $q(x)$?

   $q(x)=$
   

   What is the remainder, $r(x)$?

   $r(x)=$
   

4. Let $a(x)=5x^2-6x+10x-2$, and $b(x)=15x^3+2x$.

   When dividing $a$ by $b$, we can find the unique quotient polynomial $q$ and remainder polynomial $r$ that satisfy the following equation:

   $\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$,

   where the degree of $r(x)$ is less than the degree of $b(x)$.

   What is the quotient, $q(x)$?

   $q(x)=$

   What is the remainder, $r(x)$?

   $r(x)=$

Source: Khan Academy, https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-practice-dividing-polynomials-with-remainders/e/dividing-polynomials-with-remainders
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