Factoring Trinomials Using Grouping Method

The video tutorial explains how to factor quadratic expressions using the grouping method. It begins by introducing the concept and setting up an example problem where the expression 3x^2 + 7x + 2 is factored. The tutorial demonstrates how to find factor pairs of the product of the first and last coefficients that sum to the middle term. It then shows how to group terms and factor out common terms, leading to the final solution. The process is verified by ensuring the parentheses match, confirming the correctness of the solution.

What is the main difference between the grouping method discussed in the video and previous factoring methods?

• It requires the use of complex numbers.

• It involves dividing by the greatest common factor.

• It does not require a greatest common factor to divide out.

• It only works for quadratic equations.

In the example problem, what are the coefficients of the quadratic equation given?

• 3, 6, 1

• 1, 6, 3

• 3, 7, 2

• 2, 7, 3

What is the product of the first coefficient and the last number in the example problem?

• 8

• 7

• 6

• 5

Which pair of factors of 6 adds up to 7?

• 1 and 6

• 2 and 3

• 3 and 3

• 1 and 5

How is the middle term 7x split in the example problem?

• 2x + 6x

• 2x + 5x

• 3x + 4x

• 1x + 6x

What common term is factored out from the first group of terms (3x^2 + 1x)?

• 1

• x

• 2

• 3

What common term is factored out from the second group of terms (6x + 2)?

• 3

• x

• 2

• 1

What should be the same in both parentheses to confirm the correct grouping?

• The coefficients

• The constants

• The variables

• The terms inside the parentheses

What is the final factored form of the quadratic equation 3x^2 + 7x + 2?

• (3x + 2)(x + 1)

• (3x + 2)(x + 3)

• (3x + 1)(x + 2)

• (3x + 1)(x + 3)

What does the presence of identical parentheses indicate in the grouping method?

• The equation is fully factored correctly.

• The equation needs further simplification.

• The equation is incorrect.

• The equation is partially factored.