Greatest Common Factor in Polynomials

What is the greatest common factor of the polynomials 6x^2 - 9x and 12x^3 - 18x^2?

• 5x(2x - 3)

• 2x(3x - 4)

• 3x(2x - 3)

• 4x(3x - 2)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

Find the greatest common factor of the polynomials 4a^2b - 6ab^2 and 8ab^2 - 12a^2b.

• 6ab(2a - 3b)

• 4ab(2a - 3b)

• 10ab(2a - 3b)

• 2ab(2a - 3b)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

How can the concept of greatest common factor be applied to simplify the expression 10x^2y - 15xy^2?

• Subtract 5xy from the expression to simplify it

• Add 5xy to the expression to simplify it

• Divide by 5xy to simplify the expression

• Factor out 5xy to simplify the expression to 5xy(2x - 3y).

Tags

CCSS.7.EE.A.1

Determine the greatest common factor of the polynomials 18x^2y^2 - 27xy and 36x^3y - 54x^2y^2.

• 9xy(2x - 3y)

• 12xy(3x - 4y)

• 6xy(3x - 2y)

• 15xy(2x - 3y)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

Explain how the concept of greatest common factor can be used to simplify the expression 20a^3b^2 - 30a^2b^3.

• 10a^2b^2

• 25a^5b^5

• 15a^2b^3

• 5a^3b^2

Tags

CCSS.7.EE.A.1

If a construction company needs to pave two rectangular parking lots with dimensions 40x^2y and 60xy^2, how can the concept of greatest common factor help in optimizing the use of paving material?

• By finding the greatest common factor, the construction company can increase waste and ensure inefficient use of paving material.

• By finding the greatest common factor, the construction company can minimize waste and ensure efficient use of paving material.

• By finding the greatest common factor, the construction company can have no impact on the use of paving material.

• By finding the greatest common factor, the construction company can only optimize the use of paving material for one parking lot.

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

Find the greatest common factor of the polynomials 15a^2b^2c - 25ab^2c^2 and 30a^2bc^2 - 50ab^2c.

• 7a^2b^2c^2

• 5ab^2c

• 10a^2bc

• 3ab^2c

Tags

CCSS.HSA.APR.A.1

How can the concept of greatest common factor be applied to simplify the expression 12x^3y^2 - 18x^2y^3?

• Factor out the greatest common factor 6x^2y^2 from both terms.

• Combine the exponents of x and y in each term

• Divide each term by 6x^2y^2

• Add the coefficients of the terms

Tags

CCSS.7.EE.A.1