Factoring GCF and Solving Techniques

The video tutorial introduces factoring and its importance in solving polynomial equations. It explains the difference between factored and standard forms, emphasizing the need for factored form to apply the zero product property. The tutorial provides examples of solving equations using this property and discusses various factoring techniques, particularly focusing on the greatest common factor. It also guides viewers on writing polynomials in factored form and verifying their solutions.

What is the primary purpose of factoring in solving polynomial equations?

• To simplify the equation

• To convert it to standard form

• To find the roots or solutions

• To eliminate variables

Which form of a polynomial equation is necessary for solving it?

• Simplified form

• Expanded form

• Factored form

• Standard form

What does the zero product property state?

• If a product is zero, the sum of the factors must be zero

• If a product is zero, both factors must be zero

• If a product is zero, one of the factors must be zero

• If a product is zero, the difference of the factors must be zero

In the equation (x - 4)(x + 2) = 0, what are the solutions for x?

• x = 4 and x = 2

• x = 4 and x = -2

• x = 0 and x = 2

• x = -4 and x = 2

What are the solutions for the equation 5x - 6 = 0?

• x = -5/6

• x = 6/5

• x = 5/6

• x = -6/5

What does factoring a polynomial involve?

• Writing it as a difference of polynomials

• Writing it as a quotient of polynomials

• Writing it as a product of polynomials

• Writing it as a sum of polynomials

What is the greatest common factor (GCF) of 12x^2 and 24xy?

• 6x

• 12x

• 24x

• 12xy

What is the GCF of 6n^2 and 15n?

• 2n

• 15n

• 6n

• 3n

In the equation 4x^3(x + 6) = 0, what are the solutions for x?

• x = 0 and x = -6

• x = 4 and x = 6

• x = 0 and x = 6

• x = -4 and x = -6

How can you verify if you have factored a polynomial correctly?

• By adding the factors

• By subtracting the factors

• By dividing the factors

• By multiplying the factors back together