Factoring Polynomials and GCF

This video tutorial covers the process of factoring polynomials, focusing on finding the greatest common factor (GCF) and using the distributive property. It begins with an introduction to the prerequisites, such as prime factorization and the distributive property. The tutorial then provides detailed examples of factoring binomials and more complex polynomials, emphasizing the importance of checking work using the distributive property. The video aims to equip students with the skills to factor polynomials effectively.

What is the first step in factoring polynomials?

• Finding the least common multiple

• Identifying the greatest common factor

• Applying the Pythagorean theorem

• Using the quadratic formula

Which of the following is necessary before factoring polynomials?

• Knowledge of prime factorization

• Ability to solve linear equations

• Understanding calculus

• Familiarity with trigonometry

What is the prime factorization of 81?

• 2 * 2 * 2 * 2

• 5 * 5 * 5

• 7 * 7

• 3 * 3 * 3 * 3

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

• By adding the terms

• By subtracting the smaller term from the larger

• By listing and comparing their prime factors

• By dividing the larger term by the smaller

What is the greatest common factor of 81y^2 and 144y^3?

• 12y^3

• 81y^3

• 9y^2

• 3y^2

What does the distributive property allow you to do?

• Divide terms inside parentheses

• Subtract terms inside parentheses

• Multiply a term outside the parentheses with each term inside

• Add terms inside parentheses

In the expression 2(x + 2), what is the result of applying the distributive property?

• 2x + 2

• 4x + 4

• 2x + 4

• 4x + 2

What is the greatest common factor of 12x^2 and 15x^3?

• 3x

• 3x^2

• 6x^2

• 15x^3

When factoring 12x^2 and 15x^3, what is left after factoring out the GCF?

• 2x and 3x

• 4 and 5x

• 3 and 5x

• 6 and 3x

Why is it important to remember the number 1 when all terms are factored out?

• It is used in division

• It simplifies the expression

• It ensures the expression can be reconstructed

• It helps in adding terms