Math Problem Statement
Solution
Let's go through the problem step-by-step:
Part (a): Factorize
We need to factorize the quadratic expression .
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Look for two numbers that multiply to 12 and add up to 7. These numbers are 3 and 4, since:
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Rewrite the expression as a product of two binomials:
So, the factorization of is:
Part (b): Solve
To solve the equation , we can use the factors we found in part (a).
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Set each factor equal to zero:
- or
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Solve for in each case:
So, the solutions to the equation are:
Would you like more details, or do you have any other questions?
Related Questions to Explore:
- How can we factorize other quadratic expressions with different coefficients?
- What if the quadratic expression cannot be factorized easily—how else can we solve it?
- How does the quadratic formula apply to this problem?
- Why does factoring work as a method for solving quadratic equations?
- Can these methods apply to higher-degree polynomials?
Tip:
When factoring quadratics, look for factor pairs that match both the product and sum conditions for quick factorization.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring Quadratics
Solving Quadratic Equations
Formulas
Factoring by finding factors that add to the middle term and multiply to the constant term
Theorems
Zero Product Property
Suitable Grade Level
Grades 7-9