Factor by Grouping Concepts

The video tutorial explains the technique of factoring polynomials by grouping. It highlights the importance of identifying a common binomial factor and demonstrates the process through two examples. The first example involves factoring a polynomial with terms that share a common factor, while the second example shows how to handle terms without obvious common factors. The tutorial emphasizes the need to verify the factored form by multiplying the factors back together.

What is the key requirement for factor by grouping to be successful?

• Using only positive coefficients

• Having an even number of terms

• Starting with a quadratic polynomial

• Having a common binomial factor

When dividing a polynomial for factor by grouping, how many terms should each group ideally have?

• One term

• Three terms

• Two terms

• Four terms

What is the greatest common factor of 8x^3 and 12x^2?

• 2x

• 12x^2

• 4x^2

• 8x^3

In the example, what binomial factor is common in both groups after factoring?

• 2x - 3

• x - 3

• x + 2

• 4x^2 - 3

What is the greatest common factor of 3z^3 and -3z^2?

• z^2

• 3z^2

• 3z^3

• -3z^2

What should be factored out from z + 1 to maintain a common binomial factor?

• z

• 1

• z + 1

• z - 1

What is the resulting polynomial after factoring out the common binomial factor z - 1?

• 3z^2 + 1

• z^3 + 3

• 3z^3 + 1

• z^2 + 3

Why is it important to verify the factored polynomial?

• To confirm the correct factors were used

• To make sure the polynomial is quadratic

• To ensure the polynomial is simplified

• To check for any missing terms

What operation can be used to verify the correctness of the factored polynomial?

• Division

• Subtraction

• Multiplication

• Addition

What is the final step in the factor by grouping process?

• Checking the factored polynomial

• Factoring out the common binomial factor

• Dividing the polynomial into groups

• Identifying the greatest common factor