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Complete Question
Students in a pre-algebra class are given the polynomial 12x²y - 6xy +18y² and told to factor out the greatest common factor.
Which student has made the correct choice? (1 point)
a) Delia chose 3y because she said that it was a factor of every term.
b) Pedro chose y because he said that the greatest common factor can be found only by looking at the variable terms.
c) Mike chose 6y because he said that it was the largest factor of every term. d) Marisol chose 6 because she said that it was the only greatest common factor in each term.
Answer:
c) Mike chose 6y because he said that it was the largest factor of every term.
Explanation:
Step 1
Identify the GCF of the coefficients.
12x²y - 6xy + 18y²
Coefficients are :
12, 6, 18
The Greatest Common Factor for 12, 6, 18 =
The factors of 6 are: 1, 2, 3, 6
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 6.
Step 2
Identify the GCF of the variables.
x²y , xy, y²
The GCF of these variables is y
Step 3
Combine to both GCF's to obtain the GCF of the expression.
= 6 × y
= 6y
The Greatest Common Factor for the expression 12x²y−6xy + 18y² is 6y
Step 4
We factorise
= 12x²y−6xy + 18y²
= 6y(2x² - x + 3y)
Therefore, Option c) Mike chose 6y because he said that it was the largest factor of every term is the correct option.
Mike is correct.