1) Find a polynomial $q(x)$ such that $(x+1)^3+x^2\cdot q(x)$ has degree less than $2$.

2) Find all integers $n$ for which $\frac{n^2+n+1}{n-1}$ is an integer.

3) Find the quotient and remainder when $x^2+2$ is divided by $x-2$.

4) Find the quotient and remainder when $9x^4+x^3-12x+21$ is divided by $x+4$

5) Find the quotient and remainder when $t^4-t^2+3t-7$ is divided by $t^2-3t+8$.

6) The polynomial $4x^3 - 20x^2 + 19x + 15$ has a root at $x = 3$. Find the other two roots.

7) Given that $x=2$ is a root of $p(x)=x^4-3x^3+6x^2-12x+8$, find the other roots (real and nonreal).

8) When $x^3 + 30x - c$ is divided by $x - 5$ the remainder is 5. What is $c$?

9) When $x^4 + 6x^3 - ax^2 - 45 x - 15$ is divided by $x^2 - x - 6$ the remainder is 3. What is $a$?

10) Find the remainder when $r^{13} + 1$ is divided by $r - 1$.

ET3.1415 Apr 26, 2019

#1**0 **

Seriously??? TEN questions in a single post? No attempt on your part to answer ANY of these? We are not here to give answers to your homework or test questions!

TRY to answer them ....THEN post a single question at a time....

ElectricPavlov Apr 26, 2019

#3**-1 **

Person, please stop using this as a cheat site. It is already obvious at this point, you clearly have an inability to do your own homework so please stop using this as a cheat site and try solving these problems on your own please.

If you still need help you can always ask us to verify your answers or tell your what you have done wrong.

doorknoob Apr 26, 2019