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What is the correct answer when you factorise 3x - 9?- a)3(x - 3)
- b)3(x + 3)
- c)x(3 - 3)
- d)x(3 + 3)
Correct answer is option 'A'. Can you explain this answer?
a)
3(x - 3)
b)
3(x + 3)
c)
x(3 - 3)
d)
x(3 + 3)
 | Abhay Menon answered |
Understanding Factorization
Factorization is the process of breaking down an expression into simpler components, or factors, that when multiplied together produce the original expression. In this case, we are looking at the expression 3x - 9.
Step-by-Step Factorization
1. Identify Common Factors
The expression 3x - 9 has common factors that can be extracted. Both terms (3x and -9) share a common factor of 3.
2. Extract the Common Factor
When we factor out 3 from each term:
- 3x becomes 3(x)
- -9 becomes 3(-3)
3. Rewrite the Expression
Thus, we can rewrite the expression as:
- 3(x - 3)
Conclusion
Therefore, the completely factored form of 3x - 9 is:
- 3(x - 3)
This matches option 'A' from your choices.
Why the Other Options are Incorrect
- Option B (3(x + 3)): Adds incorrectly to the factors.
- Option C (x(3 - 3)): Incorrectly implies a factor of zero, which is not a valid factorization.
- Option D (x(3 + 3)): Wrongly introduces x instead of factoring out the correct common factor.
Final Answer
The correct answer is indeed option 'A': 3(x - 3). This factorization represents the original expression accurately and is a fundamental skill in algebra.
Factorization is the process of breaking down an expression into simpler components, or factors, that when multiplied together produce the original expression. In this case, we are looking at the expression 3x - 9.
Step-by-Step Factorization
1. Identify Common Factors
The expression 3x - 9 has common factors that can be extracted. Both terms (3x and -9) share a common factor of 3.
2. Extract the Common Factor
When we factor out 3 from each term:
- 3x becomes 3(x)
- -9 becomes 3(-3)
3. Rewrite the Expression
Thus, we can rewrite the expression as:
- 3(x - 3)
Conclusion
Therefore, the completely factored form of 3x - 9 is:
- 3(x - 3)
This matches option 'A' from your choices.
Why the Other Options are Incorrect
- Option B (3(x + 3)): Adds incorrectly to the factors.
- Option C (x(3 - 3)): Incorrectly implies a factor of zero, which is not a valid factorization.
- Option D (x(3 + 3)): Wrongly introduces x instead of factoring out the correct common factor.
Final Answer
The correct answer is indeed option 'A': 3(x - 3). This factorization represents the original expression accurately and is a fundamental skill in algebra.
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