Greatest Common Factor and Factoring

The video tutorial explains how to factor trinomials with non-unit leading coefficients. It emphasizes the importance of identifying the greatest common factor (GCF) as the first step in the factoring process. Through four examples, the tutorial demonstrates how to factor trinomials by first extracting the GCF and then further factoring the resulting expression. Each example highlights the process of identifying factors that add up to a specific term, ensuring a comprehensive understanding of the factoring process.

What is the first step in factoring trinomials when the leading coefficient is not 1?

• Combine like terms.

• Look for the greatest common factor.

• Find the factors of the constant term.

• Divide the trinomial by the leading coefficient.

In the example 2x^2 - 8x - 42, what is the greatest common factor?

• 2

• 8

• 1

• 4

After factoring out the GCF in 2x^2 - 8x - 42, what is the resulting trinomial?

• x^2 - 2x - 21

• 2x^2 - 4x - 21

• x^2 - 4x - 21

• x^2 - 8x - 42

In the trinomial 5x^2 - 35x + 50, what is the greatest common factor?

• 5

• 1

• 10

• 15

What are the binomial factors of x^2 - 7x + 10?

• (x + 7)(x - 10)

• (x - 7)(x + 10)

• (x + 5)(x + 2)

• (x - 5)(x - 2)

For the trinomial 4x^2 + 36x + 56, what is the greatest common factor?

• 4

• 8

• 2

• 12

What are the binomial factors of x^2 + 9x + 14?

• (x - 9)(x - 14)

• (x + 9)(x + 14)

• (x - 7)(x - 2)

• (x + 7)(x + 2)

In the example 4x^3 + 16x^2 - 20x, what is the greatest common factor?

• x

• 4

• 20

• 4x

What are the binomial factors of x^2 + 4x - 5?

• (x + 4)(x - 5)

• (x + 5)(x - 1)

• (x - 4)(x + 5)

• (x - 5)(x + 1)

Why is it important to find the greatest common factor first in factoring?

• It increases the degree of the polynomial.

• It eliminates the need for further factoring.

• It changes the leading coefficient to zero.

• It simplifies the expression.