Math Problem Statement
Factor the given expression completely: 7z^2 - 15z + 2
Solution
The given expression is:
To factor this, let’s proceed step by step:
Step 1: Multiply the leading coefficient and the constant term
The leading coefficient is , and the constant term is . Their product is:
Step 2: Find two numbers that multiply to and add to
The two numbers are and , since:
Step 3: Rewrite the middle term using these numbers
Rewrite as :
Step 4: Group and factor each group
Group the terms into two pairs:
Factor out the greatest common factor (GCF) from each group:
Step 5: Factor out the common binomial factor
Final Answer:
The completely factored form of is:
Let me know if you’d like further explanation or help with related questions!
5 Related Questions:
- How do you check if a quadratic expression is factorable or prime?
- What is the process for factoring when the leading coefficient is greater than ?
- How do you determine the greatest common factor (GCF) in a polynomial?
- What is the role of the discriminant in checking factorability of quadratic equations?
- Can all quadratic expressions be factored over integers?
Tip:
Always check your factors by expanding them back to the original expression to ensure correctness!
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring Quadratics
Grouping Method
Formulas
Standard quadratic form: ax^2 + bx + c
Factoring method: Find two numbers that multiply to ac and add to b
Theorems
Distributive Property
Suitable Grade Level
Grades 9-11