Factoring Polynomials by Grouping

The video tutorial explains how to factor polynomials by grouping. It begins by identifying when to use this method, specifically when dealing with four terms. The process involves grouping terms, factoring out the greatest common factor from each group, and then combining the results to achieve the final factored form. The tutorial provides a step-by-step guide, demonstrating the factoring of each group and the final combination to reach the solution.

What is a key indicator that you should use factoring by grouping?

• The polynomial has four terms.

• The polynomial is a quadratic.

• The polynomial has a leading coefficient of 1.

• The polynomial is a perfect square.

How many terms should a polynomial have to consider factoring by grouping?

• Three

• Five

• Two

• Four

What is the first step in factoring by grouping?

• Combine like terms.

• Divide the polynomial by a monomial.

• Multiply the terms.

• Factor out the greatest common factor from the first group.

What is the greatest common factor of the first group in the example?

• x

• x squared

• 2

• 3x

After factoring out x squared from the first group, what expression is left?

• x + 2

• 3x - 2

• x squared - 2

• 3x + 2

What is the greatest common factor of the second group in the example?

• 3x

• x squared

• x

• 2

What expression is left after factoring out the greatest common factor from the second group?

• 3x - 2

• x squared + 2

• 3x + 2

• x + 2

What is the next step after factoring both groups?

• Add the factored terms.

• Multiply the factored terms.

• Combine the common factors.

• Divide the polynomial by a monomial.

What common factor is found in both groups after initial factoring?

• 2

• x + 2

• 3x - 2

• x squared

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

• (x squared - 2)(3x + 2)

• (x squared + 2)(3x + 2)

• (3x - 2)(x squared + 2)

• (3x - 2)(x + 2)