Solutions to Problem Set 12

Math 101-06

10-4-2017

[Polynomial division]

1. Find the quotient and remainder when $2 x^2 - 5 x + 7$ is divided by $x
   + 3$ .

$$\hbox{\epsfysize=1.5in \epsffile{polynomial-division1.eps}}\quad\halmos$$


2. Find the quotient and remainder when $2 x^2 + 11 x + 5$ is divided by $x
   + 5$ .

$$\hbox{\epsfysize=1.5in \epsffile{polynomial-division2.eps}}\quad\halmos$$


3. Find the quotient and remainder when $2 x^3 + 5 x - 3$ is divided by $x
   + 2$ .

$$\hbox{\epsfysize=1.5in \epsffile{polynomial-division3.eps}}\quad\halmos$$


4. Find the quotient and remainder when $x^3 + 4 x^2 - 5 x + 2$ is divided by $x^2 + 1$ .

$$\hbox{\epsfysize=1.5in \epsffile{polynomial-division4.eps}}\quad\halmos$$


5. Find the quotient and remainder when $2 x^3 - x^2 - 7 x + 13$ is divided by $x + 2$ .

$$\hbox{\epsfysize=2in \epsffile{polynomial-division5.eps}}\quad\halmos$$


We'd be wise to question why we hold a grudge as if it were going to make us happy and ease our pain. It's rather like eating rat poison and thinking the rat will die. - Pema Chödrön


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