Solving Quartic and Cubic Equations

The video tutorial explains how to solve a quartic equation by finding its roots. It begins with listing possible rational roots using factors of the constant term and leading coefficient. The process continues with synthetic division to find one root, followed by reducing the equation to a cubic form. The tutorial then demonstrates solving the cubic equation and further reduces it to a quadratic equation. Finally, the video shows how to use the method of completing the square to find the remaining roots, providing a comprehensive approach to solving quartic equations.

What type of equation is being solved in this problem?

• Cubic equation

• Quartic equation

• Quadratic equation

• Linear equation

What is the first step in finding possible rational roots of a polynomial?

• Use the quadratic formula

• Divide the polynomial by x

• Graph the polynomial

• Look at the factors of the constant term

Which of the following is a factor of 4?

• 2

• 6

• 3

• 5

What is the purpose of synthetic division in this context?

• To factor the polynomial completely

• To graph the polynomial

• To find the degree of the polynomial

• To determine if a number is a root

What happens if the remainder is zero in synthetic division?

• The number is a root

• The polynomial is prime

• The polynomial is linear

• The number is not a root

Which number was found to be a root of the quartic equation?

• 1

• -2

• 2

• -1

After finding a root, what is the next step in solving the quartic equation?

• Use the quadratic formula

• Reduce the equation to a cubic

• Graph the equation

• Check for symmetry

What is the next step after reducing the quartic equation to a cubic equation?

• Graph the cubic equation

• Check for symmetry

• Solve the cubic equation

• Use the quadratic formula

What method is used to solve the quadratic equation in this problem?

• Using the quadratic formula

• Completing the square

• Factoring

• Graphing

What is the result of completing the square for the quadratic equation?

• x = -1 ± √2

• x = 0

• x = 2

• x = 1 ± √2