Factoring and Solving Polynomial Equations

The video tutorial explains how to solve a polynomial equation by factoring. It begins with identifying the greatest common factor (GCF) of the terms, then factors the polynomial into a trinomial. The trinomial is further factored into binomials, and the zero property is used to find the solutions. The concept of solution multiplicity is also discussed, highlighting double roots.

What is the first step in solving a polynomial equation by factoring?

• Finding the roots

• Simplifying the equation

• Factoring out the greatest common factor

• Expanding the polynomial

Which number is the greatest common factor of the terms in the polynomial 6x^4 - 6x^3 - 252x^2?

• 12x^2

• 6x^2

• 3x^2

• 18x^2

After factoring out the greatest common factor, what expression is left inside the parentheses?

• x^2 - x + 42

• x^2 - x - 42

• x^2 + x - 42

• x^2 + x + 42

What are the factors of the trinomial x^2 - x - 42?

• (x + 7)(x - 6)

• (x - 6)(x + 7)

• (x + 6)(x - 7)

• (x - 7)(x + 6)

What property is used to solve the equation once it is factored?

• Zero Product Property

• Commutative Property

• Associative Property

• Distributive Property

What is one of the solutions to the equation 6x^2 = 0?

• x = 0

• x = 6

• x = 7

• x = -6

What is the solution to the equation x - 7 = 0?

• x = 7

• x = -6

• x = 0

• x = 6

What is the solution to the equation x + 6 = 0?

• x = 7

• x = 6

• x = 0

• x = -6

What term describes a solution that appears more than once in the factored form of a polynomial?

• Quadruple root

• Triple root

• Double root

• Single root

How many solutions does the polynomial equation have?

• One

• Four

• Two

• Three