Solving Polynomial Equations

The video tutorial explains how to solve a degree 6 equation by using substitution to transform it into a quadratic form. The equation is factored, and real solutions are found by solving the factored form. The solutions are verified to ensure they satisfy the original equation. The process involves understanding substitution, factoring, and solving for real solutions using cube roots.

What is the degree of the given polynomial equation?

• 9

• 6

• 3

• 2

In the substitution process, what does 'u' represent?

• x to the ninth

• x to the sixth

• x cubed

• x squared

What are the factors of the quadratic equation after substitution?

• u + 9 and u - 4

• u + 9 and u + 4

• u - 9 and u - 4

• u - 9 and u + 4

What is the next step after factoring the quadratic equation?

• Solve for u

• Re-substitute to solve for x

• Check for complex solutions

• Graph the equation

What is the real solution for x when x cubed equals 9?

• x = 3

• x = 1/3

• x = 9

• x = cube root of 9

What is the real solution for x when x cubed equals 4?

• x = 1/4

• x = 2

• x = 4

• x = cube root of 4

How do we verify the solutions satisfy the original equation?

• By solving a different equation

• By graphing the solutions

• By substituting back into the original equation

• By checking with a calculator

What property is used to simplify the expression during verification?

• Division property

• Exponent property

• Multiplication property

• Addition property

What is the result when verifying the solution x = cube root of 9?

• The expression equals 0

• The expression equals 9

• The expression equals 4

• The expression equals 1

What is the result when verifying the solution x = cube root of 4?

• The expression equals 9

• The expression equals 1

• The expression equals 0

• The expression equals 4