Math Problem Statement
Factorize 6x^2 + 11x - 10.
Solution
The problem given in the image asks to factorize the quadratic expression:
Let's go step by step to factorize it.
Step 1: Multiply the coefficient of (which is 6) by the constant term (which is -10).
Step 2: Find two numbers that multiply to give -60 and add up to the middle term’s coefficient, which is 11.
The numbers are 15 and -4 because:
Step 3: Rewrite the middle term (11x) as a sum of 15x and -4x.
Step 4: Group the terms in pairs.
Step 5: Factor out the greatest common factor (GCF) from each group.
Step 6: Factor out the common binomial factor .
Thus, the factorization of is:
Would you like more details or have any further questions? Here are five related questions you might explore:
- How do you factorize quadratics with complex solutions?
- What methods can be used to check if a factorization is correct?
- How do you solve a quadratic equation after factorization?
- How does the discriminant of a quadratic relate to factorization?
- What are some examples of quadratics that cannot be factored with real numbers?
Tip: Always check your factorization by expanding the factors to ensure they give the original quadratic expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Factoring Quadratic Expressions: ax^2 + bx + c
Theorems
Zero Product Property
Suitable Grade Level
Grades 9-10