GCF and Factoring by Grouping Explained

What is the first step in factoring any polynomial?

• Finding the greatest common factor

• Adding all coefficients

• Subtracting the exponents

• Finding the least common multiple

If you have the terms 12, 15, and 27, what is the GCF?

• 6

• 5

• 3

• 2

When factoring out the GCF, what operation is performed on the coefficients?

• Multiplication

• Addition

• Division

• Subtraction

In the expression 12m^2n^5, 3mn^3, and 6mn^3, what is the GCF?

• 12mn^5

• 6mn^3

• 3mn^3

• 3m^2n^5

What should you do if the first term of a polynomial is negative when factoring out the GCF?

• Multiply by a negative number

• Factor out a negative GCF

• Add a positive term

• Ignore the negative sign

What is the first step in factoring by grouping?

• Combine all terms

• Add the coefficients

• Separate the polynomial into two groups

• Multiply the terms

When factoring by grouping, what do you do after separating the polynomial into two groups?

• Subtract the groups

• Find the GCF of each group

• Add the groups together

• Multiply the groups

In the expression y^2 + y + x(y + 1), what is the common factor?

• y

• y^2

• x

• y + 1

What should you do if the first term in a group is negative when factoring by grouping?

• Ignore the negative sign

• Factor out a negative number

• Add a positive term

• Multiply by a negative number

In the expression 2x^3 - x^2 + 8x - 4, what is the GCF?

• 8

• 4

• 2

• x