Common Factors and Trinomial Factoring

What are the common factors of 12 and 18?

• 15, 16, 17, 19

• 10, 11, 13, 14

• 4, 5, 7, 9

• 1, 2, 3, 6

Answer explanation

The common factors of 12 and 18 are 1, 2, 3, and 6. These numbers divide both 12 and 18 without leaving a remainder.

Tags

CCSS.6.NS.B.4

Factorize the trinomial: 2x^2 + 7x + 3.

• (2x - 1)(x - 3)

• (2x + 1)(x + 3)

• (2x + 3)(x + 1)

• (2x + 2)(x + 2)

Answer explanation

To factorize the trinomial 2x^2 + 7x + 3, we look for two binomials that multiply to give the trinomial. The correct choice is (2x + 1)(x + 3) because when we expand this expression, we get 2x^2 + 7x + 3, which matches the original trinomial.

Tags

CCSS.6.EE.A.3

CCSS.6.EE.A.4

Find the common factors of 24 and 36.

• 2, 4, 8, 16, 32

• 1, 2, 3, 8, 9

• 5, 7, 11, 13, 17

• 2, 3, 4, 6, 12

Answer explanation

The common factors of 24 and 36 are 2, 3, 4, 6, and 12. These numbers can divide both 24 and 36 without leaving a remainder.

Tags

CCSS.6.NS.B.4

Factorize the trinomial: 3x^2 - 10x + 8

• (3x-4)(x-2)

• (3x+2)(x-4)

• (3x-2)(x-4)

• (3x+4)(x-2)

Answer explanation

The correct factorization of the trinomial is (3x-4)(x-2). This choice is obtained by factoring out the common factors and finding the binomials that multiply to give the trinomial.

Tags

CCSS.6.EE.A.3

CCSS.6.EE.A.4

What are the common factors of 15 and 25?

• 1, 3, 5

• 2, 5

• 1, 5

• 3, 5

Answer explanation

The common factors of 15 and 25 are 1 and 5. The correct choice is 1, 5.

Tags

CCSS.6.NS.B.4

Factorize the trinomial: 4x^2 + 12x + 9.

• (4x + 3)(x + 3)

• (2x + 4)(2x + 5)

• (2x + 1)(2x + 9)

• (2x + 3)(2x + 3)

Answer explanation

To factorize the trinomial 4x^2 + 12x + 9, we look for two binomials that multiply to give the trinomial. The correct choice is (2x + 3)(2x + 3) because when we expand it, we get 4x^2 + 12x + 9, which matches the original trinomial.

Tags

CCSS.6.EE.A.3

CCSS.6.EE.A.4

Find the common factors of 40 and 60.

• 15, 8, 3

• 30, 25, 12

• 20, 10, 5, 2, 1

• 7, 4, 2

Answer explanation

The common factors of 40 and 60 are 20, 10, 5, 2, and 1. These numbers can divide both 40 and 60 without leaving a remainder.

Tags

CCSS.6.NS.B.4

Factorize the trinomial: 5x^2 - 9x - 8.

• (5x-8)(x-8)

• (5x+8)(x-5)

• (5x-8)(x+5)

• (5x-8)(x-5)

Answer explanation

The correct choice is (5x+8)(x-5) because it is the only option that factors the trinomial correctly.

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

What are the common factors of 28 and 42?

• 4, 8, 16, 32

• 3, 6, 9, 12

• 1, 2, 7, 14

• 5, 10, 15, 20

Answer explanation

The common factors of 28 and 42 are 1, 2, 7, and 14.

Tags

CCSS.6.NS.B.4

Factorize the trinomial: 6x^2 + 11x - 10.

• (2x - 5)(3x + 2)

• (6x + 5)(x - 2)

• (2x + 5)(3x - 2)

• (3x + 2)(2x - 5)

Answer explanation

The correct factorization of the trinomial is (2x + 5)(3x - 2).

Tags

CCSS.6.EE.A.3

CCSS.6.EE.A.4