Question
A student was asked to factor 3x^2+12x+9
. Their work is shown below:
Student's Work
Step 1: Identify the GCF as 3.
Step 2: Factor out the GCF: 3x^2+12x+9 = 3(x^2+4x+3)
Step 3: Factor x^2+4x+3: 3(x^2+4x+3) = 3(x+3)(x+1)
Final Answer: 3(x+3)(x+1)
What error, if any, did the student make in their factoring process?
(1 point)
Responses
The student did not correctly identify the GCF.
The student did not correctly identify the GCF.
The student made a mistake factoring x2+4x+3
.
The student made a mistake factoring x squared plus 4 x plus 3 .
The student's answer is completely correct.
The student's answer is completely correct.
The student factored out the GCF but forgot to apply it to the final answer.
The student factored out the GCF but forgot to apply it to the final answer.
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. Their work is shown below:
Student's Work
Step 1: Identify the GCF as 3.
Step 2: Factor out the GCF: 3x^2+12x+9 = 3(x^2+4x+3)
Step 3: Factor x^2+4x+3: 3(x^2+4x+3) = 3(x+3)(x+1)
Final Answer: 3(x+3)(x+1)
What error, if any, did the student make in their factoring process?
(1 point)
Responses
The student did not correctly identify the GCF.
The student did not correctly identify the GCF.
The student made a mistake factoring x2+4x+3
.
The student made a mistake factoring x squared plus 4 x plus 3 .
The student's answer is completely correct.
The student's answer is completely correct.
The student factored out the GCF but forgot to apply it to the final answer.
The student factored out the GCF but forgot to apply it to the final answer.
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page 4 of 4
Answers
Answered by
GPT-4o mini
The student made a mistake factoring \( x^2 + 4x + 3 \).
When factoring \( x^2 + 4x + 3 \), the correct factorization is \( (x + 3)(x + 1) \), which the student correctly identified. However, the factors were not properly derived in terms of the roots of the quadratic equation and checked.
Let's verify:
1. The quadratic \( x^2 + 4x + 3 \) can be found by multiplying \( (x + 1)(x + 3) \) to get:
\[
(x + 1)(x + 3) = x^2 + 3x + 1x + 3 = x^2 + 4x + 3,
\]
which is correct.
So, no error was made regarding the initial factoring of \( x^2 + 4x + 3 \).
Therefore, the final answer the student provided, \( 3(x + 3)(x + 1) \), is correct.
The correct response is:
**The student's answer is completely correct.**
When factoring \( x^2 + 4x + 3 \), the correct factorization is \( (x + 3)(x + 1) \), which the student correctly identified. However, the factors were not properly derived in terms of the roots of the quadratic equation and checked.
Let's verify:
1. The quadratic \( x^2 + 4x + 3 \) can be found by multiplying \( (x + 1)(x + 3) \) to get:
\[
(x + 1)(x + 3) = x^2 + 3x + 1x + 3 = x^2 + 4x + 3,
\]
which is correct.
So, no error was made regarding the initial factoring of \( x^2 + 4x + 3 \).
Therefore, the final answer the student provided, \( 3(x + 3)(x + 1) \), is correct.
The correct response is:
**The student's answer is completely correct.**
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