Factoring and Polynomial Questions

What is the greatest common factor of (3x + 6y)?

• 2

• 3

• 5

• 6

Answer explanation

To find the greatest common factor of (3x + 6y), we factor out the common term. Both terms share a factor of 3, so the greatest common factor is 3.

Tags

CCSS.7.EE.A.1

The factors of (xy + xz) are ______.

• x(y + z)

• z(x + y)

• y(x + z)

• xyz

Answer explanation

To factor the expression (xy + xz), we can factor out the common term x, resulting in x(y + z). Thus, the correct answer is x(y + z).

Tags

CCSS.7.EE.A.1

Which expression below can be factored using common monomial (GCF) factoring?

• x² - y²

• 9x² + 81y²

• x² + 7x + 12

• 3x² - 5x - 2

Answer explanation

The expression 9x² + 81y² can be factored by taking out the greatest common factor (GCF), which is 9. This results in 9(x² + 9y²). The other expressions do not have a common monomial factor.

Tags

CCSS.HSA.APR.C.4

Which expression below has factors of a sum and difference of two terms?

• x² - y²

• 9x² + 81y²

• x² + 7x + 12

• 3x² - 5x - 2

Answer explanation

The expression x² - y² is a difference of squares, which factors into (x + y)(x - y). This shows it has factors of a sum and difference of two terms, making it the correct choice.

Tags

CCSS.HSA.APR.C.4

One of the factors of 9x² - 4y² is (3x + 2y). What is the other factor?

• (3x + 2y)²

• (3x - 2y)

• (2x + 3y)

• (2x - 3y)

Answer explanation

To factor 9x² - 4y², recognize it as a difference of squares: (3x)² - (2y)². The factors are (3x + 2y)(3x - 2y). Since (3x + 2y) is given, the other factor is (3x - 2y).

Tags

CCSS.HSA.APR.C.4

What are the factors of (49m² - 64n²)?

• (7 + 8n)(7 - 8n)²

• (7m + 8n)(7m + 8n)

• (7m - 8n)(7m - 8n)

• (7m + 8n)(7m - 8n)

Answer explanation

The expression 49m² - 64n² is a difference of squares, which factors as (7m + 8n)(7m - 8n). This matches the correct choice, as the other options do not represent the correct factorization.

Tags

CCSS.HSA.APR.C.4

Which polynomial has the factors of (2x - 1)(4x² + 2x + 1)?

• (6x³ - 1)

• 4x²

• 8x³ + 4x² - 4x - 1

• 8x³ - 1

Answer explanation

To find the polynomial with the factors (2x - 1)(4x^2 + 2x + 1), we multiply them. The result simplifies to 8x^3 - 1, which matches the correct answer choice.

Tags

CCSS.HSA.APR.C.4

If (x + 3) is one of the factors of (x³ + 27y³), what is the other factor?

• (x² + 9y²)

• (x² + 3xy + 9y²)

• (x² - 9y²)

• (x² - 3xy + 9y²)

Answer explanation

To find the other factor of (x^3 + 27y^3), we can use the factorization formula for the sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here, a = x and b = 3y, leading to the other factor being (x^2 - 3xy + 9y^2).

Tags

CCSS.HSA.APR.C.4

What must be added to (x² + 10x) to make it a perfect square trinomial?

• 10

• 15

• 20

• 25

Answer explanation

To make (x² + 10x) a perfect square trinomial, we need to add (10/2)² = 25. This gives us (x + 5)², confirming that 25 is the correct choice.

Tags

CCSS.HSA-REI.B.4B

Which of the following factors give a product of (16d² - 24d + 9)?

• (4d - 3)(4d - 3)

• (4d + 3)(4d + 3)

• (8d - 6)(8d - 3)

• (8d + 6)(8d + 3)

Answer explanation

The expression 16d² - 24d + 9 can be factored as (4d - 3)(4d - 3), which is a perfect square trinomial. The other options do not yield the correct product when multiplied.

Tags

CCSS.HSA.APR.C.4