# Honors Algebra 2: Extra Practice on Operations on Polynomials with Constant Exponents

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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In the following problems, assume no denominator equals zero.

1. $$\displaystyle 3x^{3a} + 24y^{3b}$$
2. Solution

$$\displaystyle 3\left( x^a + 2y^b \right) \left( x^{2a} - 2x^ay^b + 4y^{2b} \right)$$

3. Factor: $$\displaystyle \frac{1}{16}x^{3a} + \frac{1}{2}y^{6a}z^{9b}$$
4. Solution

$$\frac{1}{2} \left( \frac{1}{2}x^a + y^{2a}z^{3b} \right) \left( \frac{1}{4} x^{2a} - \frac{1}{2}x^ay^{2a}z^{3b} + y^{4a}z^{6b} \right)$$

5. Factor: $$\displaystyle c^{2w+1} + 2c^{w+1}$$
6. Solution

$$\displaystyle c^{w+1}\left( c^w + 2 \right)$$

7. Simplify: $$\displaystyle \frac{x^{4n+1}+x^{5n}}{x^{6n} - x^{5n+2}}$$
8. Solution

$$\displaystyle \frac{x + x^n}{x^n (x^n - x^2)}$$

9. Simplify: $$\displaystyle \frac{x^{4n} + 7x^{2n} + 12}{x^{3n} + 5x^{2n} + 4x^n + 20}$$
10. Solution

$$\displaystyle \frac{x^{2n} + 3}{x^n + 5}$$

11. Simplify: $$\displaystyle \frac{x^{6n} - y^{3n}}{x^{4n} - y^{2n}}$$
12. Solution

$$\displaystyle \frac{x^{4n} + x^{2n}y^n + y^{2n}}{x^{2n} + y^n}$$

13. Simplify: $$\displaystyle \frac{x^{2a} - y^{2b}}{4x^{2c} - 20x^c + 25} \cdot \frac{8x^c - 20}{3x^a + 3y^b}$$
14. Solution

$$\displaystyle \frac{4(x^a - y^b)}{3(2x^c - 5)}$$

15. Simplify: $$\displaystyle \frac{x^{3a} + x^{2a+1}}{x^{b+c}} \div \frac{x^{3a} - x^{a + 2}}{x^{a + 2b} - x^{2b + 1}}$$
16. Solution

$$\displaystyle \frac{x^ax^b}{x^c}$$

17. Simplify: $$\displaystyle \frac{20-x^c}{x^{2c} + 4x^c} + \frac{x^c + 10}{x^c + 4}$$
18. Solution

$$\displaystyle \frac{x^c + 5}{x^c}$$

19. Simplify: $$\displaystyle \frac{y^n}{y^n+6} - \frac{6 - 5y^n}{y^{2n} + 6y^n}$$
20. Solution

$$\displaystyle \frac{y^n-1}{y^n}$$

21. Simplify: $$\displaystyle \frac{1}{x^{3a}y^{5n}} + \frac{1}{x^{2a+4}y^{n+3}}$$
22. Solution

$$\displaystyle \frac{x^4y^3 + x^ay^{4n}}{x^{3n+4}y^{5n+3}}$$

23. $$\displaystyle \frac{5y^b}{6x^c} - \frac{2}{9x^cy^b} + \frac{4x^c}{3y^{2b}}$$
24. Solution

$$\displaystyle \frac{15y^{3b} - 4y^b + 24x^{2c}}{18x^cy^{2b}}$$

25. $$\displaystyle \frac{x^{2n+1} + 2x^{n+1} - 3xy^{2n}}{x^{2n+1} + 5x^{n+1}y^n + 6xy^{2n}}$$
26. Solution

$$\displaystyle \frac{x^n-y^n}{x^n + 2y^n}$$