Math Problem Statement
Solution
Let's go through the table and factor each polynomial step by step to find the corresponding binomial factor:
-
:
- This is a sum of cubes: , where and .
- The formula for factoring sums of cubes is:
- So, .
- The binomial factor is .
-
:
- This is again a sum of cubes: , where and .
- Using the same formula:
- The binomial factor is .
-
:
- Factor out the greatest common factor (GCF), which is :
- The binomial factor is .
-
:
- This is a difference of cubes: , where and .
- The formula for factoring differences of cubes is:
- So, .
- The binomial factor is .
-
:
- This is a sum of cubes: , where and .
- Using the sum of cubes formula:
- The binomial factor is .
Summary of Binomial Factors:
- →
- →
- →
- →
- →
Would you like further details or explanations on any of these factorizations? Here are five related questions you could explore:
- How do you factor a difference of squares?
- Can you factor the sum of squares?
- What is the general formula for factoring a cubic polynomial?
- How do you determine the greatest common factor in a polynomial?
- What are the differences between factoring a sum of cubes and a difference of cubes?
Tip: Always check if there's a common factor (GCF) before factoring more complex polynomials.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Polynomials
Sum of Cubes
Difference of Cubes
Formulas
Sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Greatest Common Factor (GCF)
Theorems
Sum of Cubes
Difference of Cubes
Suitable Grade Level
Grades 9-11
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