A student is attempting to factor a polynomial. Sample mathematical work is shown below. Which statement best applies to the sample mathematical work?
Given 3x + 6, the factors of the first term are 3 and x, and the factors of the second term are 1, 2, 3, and 6. Thus, the greatest common factor is 3. Dividing through by the greatest common factor, I get x + 3. Thus, the factored polynomial is 3(x + 3).
3(x+2)
The statement that best applies to the sample mathematical work is that the student is trying to factor a polynomial by finding the greatest common factor (GCF). In this case, the polynomial given is 3x + 6.
To find the GCF, the student identifies the factors of the first term, which are 3 and x, and the factors of the second term, which are 1, 2, 3, and 6. They determine that the greatest common factor of 3x and 6 is 3.
Next, the student divides the polynomial expression by the GCF of 3. This step involves dividing each term of the polynomial by 3. Dividing 3x by 3 gives x, and dividing 6 by 3 gives 2. Thus, the factored polynomial is x + 2.
However, the student made a mistake in the last step of their work. They incorrectly state that the factored polynomial is 3(x + 3). The correct factored form should be 3(x + 2), since the GCF was 3, not x + 3.
In summary, the student's work demonstrates an attempt to factor a polynomial by finding the GCF and then dividing each term by the GCF. The correct factored form should be 3(x + 2).