Factoring Polynomials

Question 1

What steps would you take to factor this expression?

Answer 1

1. Find the greatest common factor
2. Factor out the GCF using the distributive property

Question 2

What steps would you take to factor this by grouping?

(one variable)

Answer 2

1. Try grouping the first two terms and the last two terms
2. Factor out the GCF from each group
3. Factor out the common binomial (2w + 5)

Question 3

What steps would you take to factor this by grouping?

(two variables)

Answer 3

1. Rearrange the terms
2. Form groups
3. Factor GCF
4. Factor out the common binomial (2y + u)

Question 4

What steps would you take to factor this expression?

(Factoring a product of a quadratic trinomial and a monomial)

Answer 4

1. Remove the GCF from each term
2. Reverse FOIL the remaining terms

Question 5

How can this be written as the sum of two cubes?

Answer 5

Question 6

What is the formula for factoring the sum of two cubes?

Answer 6

Question 7

What is the formula for factoring the difference of two cubes?

Answer 7

Question 8

What steps would you take to solve this equation?

(two possible answers for variable)

Answer 8

Because one of the expressions must equal zero:

1. Solve for u - 1 = 0
2. Solve for u + 6 = 0

Question 9

What steps would you take to solve this equation?

(three possible answers for variable)

Answer 9

Because one of the expressions must equal zero:

1. Solve for -4w = 0
2. Solve for w + 6 = 0
3. Solve for w - 9 = 0

Question 10

What steps would you take to solve this equation?

(quadratic equation with leading coefficient one)

Answer 10

1. Factor equation
2. Solve for w + 1 = 0
3. Solve for w - 4 = 0

Question 11

What steps would you take to solve this equation?

(quadratic equation with leading coefficient greater than one)

Answer 11

1. Rewrite equation as pictured
2. Factor the right-hand side
3. Solve for each factored expression

Question 12

What steps would you take to factor this expression?

(factoring with repeated use of the difference of squares formula)

Answer 12

1. Factor out the greatest common factor
2. Write (16 - w⁴) as a difference of squares
3. Factor 4² - (w²)²
4. Factor 4 - w²

Question 13

What steps would you take to solve for v in this equation?

(Solving a quadratic equation needing simplification)

Answer 13

1. Rewrite equation with zero on one side
2. Use FOIL to expand (v + 3)²
3. Distribute the negative sign over the parenthesis
4. Combine like terms
5. Factor
6. Solve both (v + 6) and and (v - 4) for zero