Factoring Polynomials and GCF

The video tutorial covers the process of factoring polynomials completely, emphasizing the use of multiple factoring techniques such as finding the greatest common factor (GCF) and trinomial factoring. Two examples are provided to illustrate these methods, and the use of a graphing calculator is discussed for verifying the correctness of the factored expressions. The tutorial highlights common mistakes and provides strategies to avoid them, ensuring a comprehensive understanding of the factoring process.

What is the first step in factoring a polynomial completely?

• Divide by the smallest term

• Check if it's a perfect square

• Look for a greatest common factor

• Identify the leading coefficient

When factoring out the greatest common factor, what should you do with the exponents?

• Add them together

• Ignore them

• Use the smallest exponent

• Use the largest exponent

After factoring out the greatest common factor, what is the next step?

• Multiply the terms back together

• Factor the remaining expression into binomials

• Stop and check your work

• Use a graphing calculator

What is a common mistake when factoring completely?

• Dropping the leading coefficient

• Not checking with a calculator

• Forgetting to factor out the greatest common factor

• Using the wrong signs

What should you do if the factors of a trinomial do not give the correct middle term?

• Try different factor pairs

• Divide the factors

• Use the same factors

• Multiply the factors

Why is it important to keep the greatest common factor in front when factoring?

• It changes the expression

• It makes the expression longer

• It ensures the expression is completely factored

• It simplifies the expression

What is the result of factoring x^2 - 5x - 6?

• (x - 2)(x + 3)

• (x + 2)(x - 3)

• (x - 6)(x + 1)

• (x + 6)(x - 1)

How can you verify that your factored expression is correct using a graphing calculator?

• Look for a straight line

• Ensure the graphs are different

• Find the intersection points

• Check if the graphs overlap

What is the purpose of using a graphing calculator in factoring?

• To change the expression

• To simplify the expression

• To verify the factored expression

• To find the roots

In the second example, what is the greatest common factor of 3x^3, 15x^2, and 42x?

• x

• 15x

• 3x

• 42x