Factoring Binomials and GCF

The video tutorial explains how to factor a binomial with a difference of squares, using the example of 4x^2 - 36. It emphasizes the importance of factoring out the greatest common factor (GCF) first, which is often overlooked. The tutorial demonstrates the correct process and highlights common mistakes, such as not factoring completely. The video concludes by reinforcing the need to factor out the GCF as the first step in the factoring process.

What is the first step in factoring a binomial when dealing with a difference of squares?

• Multiply the terms

• Add the terms

• Factor out the greatest common factor

• Identify the perfect squares

In the expression 4x^2 - 36, what is the greatest common factor?

• 2

• 4

• 6

• 9

After factoring out the greatest common factor from 4x^2 - 36, what expression is left?

• x^2 - 36

• 4x^2 - 9

• 2x^2 - 18

• x^2 - 9

What are the two binomial factors of x^2 - 9?

• (x + 6)(x - 6)

• (x + 3)(x - 3)

• (x + 9)(x - 9)

• (x + 1)(x - 1)

Why is it incorrect to factor 4x^2 - 36 directly as a difference of squares without factoring out the GCF?

• It results in a non-factorable expression

• It leads to incomplete factoring

• It changes the original expression

• It is mathematically incorrect

What common factor is found in each binomial factor when 4x^2 - 36 is incorrectly factored directly?

• 4

• 2

• 6

• 3

What is the correct complete factorization of 4x^2 - 36?

• 4(x + 3)(x - 3)

• 2(x + 3)(x - 3)

• 4(x + 6)(x - 6)

• 2(x + 6)(x - 6)

What is a common error when factoring binomials with a difference of squares?

• Multiplying the terms incorrectly

• Ignoring the perfect squares

• Not factoring out the GCF first

• Factoring out the wrong GCF

What is the result of multiplying 2x + 6 by 2?

• 2x + 12

• 2x + 6

• 4x + 12

• 4x + 6

Why is it important to factor out the GCF first in the factoring process?

• To ensure complete factoring

• To avoid errors

• To simplify the expression

• All of the above