Factoring By Grouping: Key Concepts and Techniques

What is the first step in factoring by grouping?

• Combine all terms together

• Group the first two terms and the last two terms

• Find the common factor of all terms

• Divide each term by the highest coefficient

In the first example, what is the greatest common factor of the first group (8R^3 + 64R^2)?

• 8R

• 8R^2

• R^2

• 64R^2

What is the common binomial factor in the second example?

• 7

• 4P - 7

• 3P^2 + 7

• 3P^2

In the third example, why is a negative 5 factored out instead of a positive 5?

• To make the terms of the binomial positive

• To factor out the highest coefficient

• To simplify the equation

• To make the terms of the binomial negative

What is the greatest common factor in the fourth example's first group (6V^3 + 16V^2)?

• 2V

• 2V^2

• 3V

• 2V^3

In the fifth example, what is the greatest common factor among all terms?

• 3

• 7

• 5

• 6

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

• 3(7K^2 - 5)(K - 4)

• 3(7K^2 + 5)(K - 4)

• 3(7K^2 + 5)(K + 4)

• 3(7K^2 - 5)(K + 4)

In the seventh example, what is the greatest common factor in the first group (25V^3 + 5V^2)?

• 5V^3

• 25V

• 5V^2

• 5V

What is the common binomial factor in the eighth example?

• 3N - 5

• 7N^2 + 5

• 7N^2 - 5

• 3N + 5

In the tenth example, what is the greatest common factor in the first group (28V^3 + 16V^2)?

• 7V

• 4V^2

• 4V^3

• 4V