Compound Integral Expressions.

17. $x^2-4y^2-4yz-z^2$ by $x+2y+z$.

Arrange and divide:

18. $x^3-6a^3+11a^{2}x-6a{x}^2$ by $x^2+6a^2-5ax$.

19. $a^2-4b^2-9c^2+12bc$ by $a-3c+2b$.

20. $2a^3-8a+a^4+12-7a^2$ by $2+a^2-3a$.

21. $q^4+6q^3+4+12q+13q^2$ by $3q+2+q^2$.

22. $27a^3-8b^3$ by $3a-2b$.

Find the remainder when:

23. $a^4+9a^2+15-11a-7a^3$ is divided by $a-5$.

24. $7-8c^2+5c^3+8c$ is divided by $5c-3$.

25. $3+11a^3+30a^4-82a^2-5a$ is divided by $3a^2-4+2a$.

26. $2x^3-16x+10-39x^2+17x^4$ is divided by $2-5x^2-4x$.

[Miscellaneous Examples.]25.

1. Add $2a^2-3ac-3ab$; $2b^2+3ac+a^2$; $-a^2-2b^2+3ab$.

2. Subtract $3a^4-2a^{3}b+4a^2{b}^2$ from $4b^4-2a{b}^3+4a^2{b}^2$.

3. Simplify $x-y-\{z-x-(y-x+z)\}$.

4. Multiply $a^2+b^2+c^2-d^2$ by $a^2+b^2-c^2+d^2$.

5. Divide $10y^6+2-12y^5$ by $1+y^2-2y$.

6. If $a=1$, $b=2$, and $c=-3$, find the value of $a^2+b^2+c^2+2ab+2ac+2bc$.

7. Simplify $x-(y-z)-\backslash \{4y+[2y-(z-x)]\backslash \}$.

8. Multiply $a^2+b^2+c^2-ab-ac-bc$ by $a+b+c$.

9. Divide $16y^4-21x^2{y}^2+21x^{3}y-10x^4$ by $4y^2-5x^2+3xy$.

10. Add $-2a^4+3a^{3}b-4a^2{b}^2$; $2a^{3}b-3a^2{b}^2$; $7a^2{b}^2+2a^4-b^4$.

11. From $3x^3+5x-1$ take the sum of $x-5+5x^2$ and $3+4x-3x^2$.

12. The minuend is $9c^2+11c-5$, and the remainder is $6c^2-13c+7$. What is the subtrahend?

13. Find the remainder when $a^4+6b^4$ is divided by $a^2+2ab+2b^2$.