Factoring and Greatest Common Factor

The video tutorial explains how to factor out the greatest common factor (GCF) from algebraic expressions. It begins with an introduction to factoring and prime factorization, followed by a detailed breakdown of the prime factorization of specific terms. The tutorial then identifies the GCF and demonstrates how to factor it out from the given terms. Finally, it shows how to rewrite the terms using the GCF and concludes with the final steps in the factoring process.

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

• Add all the terms together.

• Write each term separately.

• Multiply all the terms.

• Identify the smallest term.

What is the purpose of using color coding in the factoring process?

• To highlight the incorrect terms.

• To confuse the viewer.

• To differentiate between different terms.

• To make it look colorful.

What is the prime factorization of the number 8?

• 2 * 2 * 2

• 3 * 3

• 4 * 2

• 2 * 3

What is the significance of the number of times a variable is multiplied by itself in the context of prime factorization?

• It has no significance.

• It changes the variable's base.

• It reduces the variable's value.

• It determines the variable's exponent.

How do you determine the greatest common factor of two terms?

• By dividing the terms.

• By subtracting the terms.

• By finding the largest common factors.

• By adding the terms.

What is the greatest common factor of 4x^4y and 8x^3y?

• 4x^3y

• x^3y

• 2x^2y

• 8x^4y

When rewriting terms using the greatest common factor, what should you do with the remaining factors?

• Ignore them.

• Add them to the GCF.

• Multiply them by the GCF.

• Subtract them from the GCF.

What is the result of factoring out the greatest common factor from an expression?

• A sum of terms.

• A product of the GCF and remaining terms.

• A difference of terms.

• A division of terms.

What does factoring out the greatest common factor achieve in an expression?

• It simplifies the expression.

• It complicates the expression.

• It makes the expression longer.

• It has no effect on the expression.

What is the opposite of factoring out in terms of the distributive property?

• Adding terms.

• Distributing terms.

• Dividing terms.

• Subtracting terms.