Factoring Polynomials by Grouping

This video tutorial covers the method of factoring polynomials by grouping. It begins with an introduction to the concept, followed by several examples demonstrating the technique. The instructor explains how to handle polynomials with coefficients and sign changes, and concludes with a method for factoring trinomials. The video aims to simplify the process of factoring complex polynomials by grouping terms and checking the results through foiling.

What is the primary method discussed for simplifying polynomials?

• Factoring by grouping

• Long division

• Synthetic division

• Square root method

What is factored out from the first two terms in the initial example?

• y^2

• 2z

• 4

• 3y

In the advanced example, what is factored out from all terms initially?

• 4

• y^2

• 3x

• 11x^2

What is the result of factoring by grouping in the advanced example?

• 11x^2(3x + 1)(3y - 1)

• x^2(3x + 1)(3y - 1)

• 11x^2(3x - 1)(3y + 1)

• x^2(3x - 1)(3y + 1)

What is the first step in factoring trinomials by grouping?

• Find the product of a and c

• Group the terms

• Identify the middle term

• Factor out the greatest common factor

What factors of -77 add up to the middle number in the example?

• -11 and 7

• 11 and -7

• -7 and 11

• 7 and -11

How is the trinomial rewritten using the sum of two factors?

• x^2 - 11x + 7x - 77

• x^2 + 11x - 7x + 77

• x^2 - 11x - 7x - 77

• x^2 + 11x + 7x + 77

What is the final factored form of the trinomial example?

• (x - 7)(x - 1)

• (x + 7)(x + 1)

• (x + 7)(x - 1)

• (x - 7)(x + 1)

In the example with a coefficient of 6 in front of the squared term, what is the product of a and c?

• 15

• 90

• -15

• -90

What is the factored form of the polynomial with a leading coefficient of 6?

• (2a + 3)(3a - 5)

• (2a - 3)(3a + 5)

• (3a - 2)(5a + 3)

• (3a + 2)(5a - 3)