Factoring Polynomials: Key Concepts and Techniques

This video tutorial by Math with Martinez covers the fundamental skills of factoring polynomials, focusing on the greatest common factor (GCF), difference of squares, sum of cubes, and difference of cubes. Each section provides a detailed explanation and example of how to identify and factor these polynomial forms, emphasizing the importance of recognizing patterns and applying mathematical properties.

What does GCF stand for in polynomial factoring?

• Greatest Calculated Figure

• Geometric Cubic Formula

• General Calculus Function

• Greatest Common Factor

What is the first step in factoring polynomials?

• Identifying the polynomial degree

• Finding the Greatest Common Factor

• Applying the quadratic formula

• Determining the coefficients

What pattern is used to factor a difference of squares?

• a^2 + b^2 = (a - b)(a + b)

• a^2 - b^2 = (a - b)^2

• a^2 + b^2 = (a + b)^2

• a^2 - b^2 = (a + b)(a - b)

Which of the following is a perfect square?

• 50

• 64

• 82

• 35

What is the result of factoring 36w^2 - 25?

• (6w + 5)(6w - 5)

• (w + 5)(w - 5)

• (36w + 25)(36w - 25)

• (6w^2 + 5)(6w^2 - 5)

What is the square root of 49?

• 5

• 6

• 7

• 8

What is the factored form of a sum of cubes?

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 - b^3 = (a + b)(a^2 - ab + b^2)

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^3 + b^3 = (a + b)^3

Which of the following is a perfect cube?

• 30

• 27

• 65

• 50

What is the cube root of 64?

• 2

• 4

• 8

• 3

How do you factor a difference of cubes?

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 - b^3 = (a + b)(a^2 - ab + b^2)

• a^3 - b^3 = (a - b)^3

• a^3 - b^3 = (a - b)(a^2 + ab + b^2)