Factoring Polynomials and Techniques

The video tutorial explains the technique of factoring polynomials by grouping. It emphasizes 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 highlights the need to divide the polynomial into two parts and factor each separately to find a common binomial factor.

What is the primary goal when using the grouping technique to factor a polynomial?

• To divide the polynomial into equal parts

• To find the greatest common factor

• To end up with a common binomial factor

• To simplify the polynomial

What is the last step in factoring by grouping?

• Dividing the polynomial into two parts

• Checking the factored terms

• Factoring out the common binomial factor

• Identifying the greatest common factor

In the first example, what is the greatest common factor of 8x^3 and 12x^2?

• 12x^2

• 2x

• 4x^2

• 8x^3

What is left after factoring out 4x^2 from 8x^3?

• 4x

• 2x

• x

• 8x

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CCSS.HSA.APR.D.6

Why is it important to check the factored terms in the first example?

• To verify the presence of a common binomial factor

• To ensure they are in simplest form

• To confirm the polynomial is divided correctly

• To check for any errors in calculation

What is the common binomial factor in the first example?

• x + 2

• 4x^2 - 3

• x - 3

• 2x - 3

In the second example, what is the greatest common factor of 3z^3 and -3z^2?

• -3z^2

• 3z^3

• 3z^2

• z

Tags

CCSS.7.EE.A.1

What should be factored out from the right side in the second example when z and 1 don't share any common factors?

• The variable z

• Zero

• Negative one

• Positive one

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CCSS.8.EE.C.7B

In the second example, what is the result after factoring out a positive one from the right side?

• z

• z + 1

• 1

• z - 1

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CCSS.HSA.APR.C.4

What is the final factored form of the polynomial in the second example?

• (z + 1)(3z^2 - 1)

• (z - 1)(3z^2 + 1)

• (z - 1)(3z^2 - 1)

• (z + 1)(3z^2 + 1)

Tags

CCSS.HSA.APR.C.4