Math Problem Statement
Fully factorize x^2 + 7x + 12 and use your answer to solve x^2 + 7x + 12 = 0.
Solution
Let's solve the problem step by step.
Part (a): Fully factorize
To factorize :
- Look for two numbers that multiply to 12 (the constant term) and add up to 7 (the coefficient of ).
The numbers are 3 and 4 because:
Thus, the factorization is:
Part (b): Solve
Using the factorization from part (a):
To solve, set each factor equal to zero:
The solutions are:
Final Answers:
- Part (a):
- Part (b):
Would you like further clarification or more examples of similar problems?
Here are 5 related questions to deepen understanding:
- How do you factorize quadratic equations with different coefficients for ?
- Can you explain why factorization helps solve quadratic equations?
- How would you solve ?
- What happens if a quadratic equation cannot be factorized neatly?
- Can we solve using the quadratic formula? Would the solutions match?
Tip: Always double-check your factorization by expanding the factors back to verify the original quadratic expression.
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Math Problem Analysis
Mathematical Concepts
Factoring Quadratic Equations
Solving Quadratic Equations
Formulas
Standard form of a quadratic equation: ax^2 + bx + c = 0
Theorems
Zero Product Property
Suitable Grade Level
Grades 7-9