(Factoring Algebraic Expressions HC)You are given the expression 30x4y3 − 12x3y.Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point)Part B: Explain how you found the common factor. (1 point)Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)
Question
(Factoring Algebraic Expressions HC)You are given the expression 30x4y3 − 12x3y.Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point)Part B: Explain how you found the common factor. (1 point)Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)
Solution
Part A: The common factor for the expression that has a coefficient other than 1 and that contains at least one variable is 6x^3y.
Part B: To find the common factor, you need to look for the highest power of x and y that appears in both terms, and the greatest common divisor of the numerical coefficients. The numerical coefficients are 30 and 12, and their greatest common divisor is 6. The highest power of x that appears in both terms is x^3, and the highest power of y that appears in both terms is y. Therefore, the common factor is 6x^3y.
Part C: To rewrite the expression using the common factor, you divide each term by the common factor.
30x^4y^3 ÷ 6x^3y = 5x^1y^2 12x^3y ÷ 6x^3y = 2
So, the expression 30x^4y^3 - 12x^3y can be rewritten as 6x^3y(5x^1y^2 - 2).
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