Math Problem Statement
answer
Solution
Let's solve the given problems by factoring the provided polynomials.
a.
We can factor out the greatest common factor (GCF) of all terms: Now, factor the quadratic inside the parentheses: Thus, the factored form is:
b.
First, factor out the greatest common factor (GCF): Now, we factor the quadratic . Look for two numbers that multiply to and add to . These numbers are and . Rewrite the middle term: Factor by grouping: Thus, the factored form is:
c.
We need to factor this quadratic. Find two numbers that multiply to and add to . These numbers are and . Rewrite the middle term: Factor by grouping: Thus, the factored form is:
d.
First, rearrange the terms in standard form: Now, factor by grouping: Factor out the common binomial factor: Notice that is a difference of squares: Thus, the factored form is:
Would you like further details on any of these factorizations or have any questions?
Here are five related questions:
- How do you factor a quadratic trinomial?
- What are the steps for factoring by grouping?
- How do you recognize a difference of squares?
- Can you always factor a cubic polynomial?
- What is the significance of finding the greatest common factor (GCF) first?
Tip: Always check for the GCF before trying more advanced factoring techniques. It simplifies the polynomial and makes the process easier.
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Math Problem Analysis
Mathematical Concepts
Factoring Polynomials
Greatest Common Factor (GCF)
Factoring by Grouping
Difference of Squares
Formulas
ax^2 + bx + c = 0 (Quadratic Formula)
Factoring by Grouping: ax^2 + bx + c → (ax + p)(bx + q)
Difference of Squares: a^2 - b^2 = (a - b)(a + b)
Theorems
Quadratic Theorem
Difference of Squares Theorem
Greatest Common Factor (GCF) Method
Suitable Grade Level
Grades 9-12
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