Finding vertex and intercepts

Question

Assignment:

Q1. Write the polynomial in descending order and find the degree:   x² - x⁵ + 2x⁴ - 1

Q2. Subtract 3x -5 + 2x³ from   3x³ - 1

Q3. Multiply: (9x - 2) (x + 4)

Q4. Multiply (5x - 6y) (5x + 6y)

Q5. Simplify (-12a⁷b⁰c² / 3a³b²c⁶)^-3

Q6. Divide:  x³ + 5x² - 10 by x + 3

Q7. Factor:  10x⁶ - 15x⁴ + 2x³ - 3x

Q8. Factor:  x² - 16 = (x - 4) (x + 4)

Q9. Factor: 16x³ - 24x² + 9x

Q10. Solve for x: 5x² + 33x - 14 = 0

Q11. Simplify: x² + 5x - 24 / x² - 64

Q12. Divide:  2x² + 9x + 10 / 2x² + 3x + 5 ÷ x² + 5x + 6 / 2x² + 4x -6

Q13. Simplify: (-3 / 4 - x) - (5 / x - 4)

Q14. Solve: x - 5 / x + 7 = x + 4 / x + 6

Q15. Solve: √(x - 7) - √x = -1

Q16. Solve: (x - 6)² = 10

Q17. Solve by completing the square: 3x² - 2x + 5 = 0

Q18. Solve (x - 4)² = - 81

Q19. Solve 2x² - 4x + 9 = 0

Q20. Find the vertex and intercepts of: y = - x² + 6x - 11

Provide complete and step by step solution for the question and show calculations and use formulas.