Factoring Quartic Binomials with Common Factors

The video tutorial explains how to factor out the greatest common factor (GCF) from an algebraic expression. It begins with an introduction to the concept of factoring and the GCF, followed by a detailed explanation of prime factorization of the terms involved. The tutorial then identifies the common factors and demonstrates the process of factoring out the GCF. Finally, it simplifies the expression, showing the steps involved in the process. The tutorial aims to make the concept clear and understandable, providing both a detailed breakdown and a quicker mental method for factoring.

What is the first step in factoring out the greatest common factor?

• Simplifying the expression

• Finding the prime factorization of each term

• Multiplying the terms

• Adding the coefficients

What is the prime factorization of 4x to the fourth y?

• 2 * 2 * 2 * x * x * x * x * y

• 2 * 2 * x * x * x * x * y

• 2 * 2 * 2 * x * x * x * y

• 2 * 2 * x * x * y

How many 2's are common in the prime factorizations of 4 and 8?

• One

• Two

• Three

• None

What is the greatest common factor of 4x to the fourth y and 8x to the third y?

• 8x to the third y

• 4x to the third y

• 4x to the fourth y

• 2x to the third y

What do you get when you divide 4x to the fourth y by 4x to the third y?

• x

• 4x

• 8x

• 2x

What is left when you factor out 4x to the third y from 8x to the third y?

• x

• 2

• 4

• 8

What is the simplified form of the expression after factoring out the greatest common factor?

• 4x to the fourth y (x + 2)

• 8x to the third y (x + 2)

• 4x to the third y (x + 2)

• 4x to the third y (x + 4)

What is the purpose of factoring out the greatest common factor?

• To divide the terms

• To simplify the expression

• To make the expression more complex

• To add the terms together

What happens to the expression when you factor out the greatest common factor?

• It becomes more complex

• It remains the same

• It gets simplified

• It gets multiplied

What is the result of dividing 8 by 4 in the context of factoring out the greatest common factor?

• 2

• 8

• 4

• 1