Factoring and Distributing Polynomials

Factor the expression: 3x^2 + 6x

• x(3x + 6)

• 3x(x + 2)

• 3(x^2 + 2x)

• 3x^2 + 2

Answer explanation

To factor 3x^2 + 6x, we can factor out the greatest common factor, which is 3x. This gives us 3x(x + 2), making it the correct choice. The other options do not represent the factored form of the expression.

Distribute: 5(2x + 3)

• 5(2x) + 3

• 10x + 15

• 10x + 3

• 5(2x + 5)

Answer explanation

To distribute 5(2x + 3), multiply 5 by each term inside the parentheses: 5 * 2x = 10x and 5 * 3 = 15. Thus, the expression simplifies to 10x + 15, which is the correct answer.

Tags

CCSS.6.EE.A.3

Combine like terms: 4x + 3x - 2

• 5x - 2

• 4x + 3

• 7x + 2

• 7x - 2

Answer explanation

To combine like terms, add the coefficients of x: 4x + 3x = 7x. The constant term remains -2. Thus, the final expression is 7x - 2, which matches the correct answer.

Tags

CCSS.7.EE.A.1

Factor: x^2 - 9

• (x - 1)(x + 1)

• (x - 4)(x + 4)

• (x - 3)(x + 3)

• (x - 2)(x + 2)

Answer explanation

To factor x^2 - 9, recognize it as a difference of squares: a^2 - b^2 = (a - b)(a + b). Here, a = x and b = 3, so it factors to (x - 3)(x + 3). Thus, the correct choice is (x - 3)(x + 3).

Tags

CCSS.HSA.APR.C.4

Distribute: 2(x + 4) - 3(x - 2)

• -2x + 10

• 2x + 8

• x + 6

• -x + 14

Answer explanation

Distributing gives: 2x + 8 - 3x + 6. Combining like terms results in -x + 14, which matches the correct answer.

Tags

CCSS.6.EE.A.3

Combine like terms: 7y - 2y + 5

• 7y + 5

• 5y - 2

• 2y + 5

• 5y + 5

Answer explanation

To combine like terms, subtract 2y from 7y, which gives 5y. The constant term remains 5. Thus, the expression simplifies to 5y + 5, making '5y + 5' the correct answer.

Tags

CCSS.7.EE.A.1

Factor: 2x^2 + 8x

• 2x(x + 4)

• 4x(x + 2)

• x(2x + 8)

• 2(x^2 + 4x)

Answer explanation

To factor 2x^2 + 8x, we can factor out the greatest common factor, which is 2x. This gives us 2x(x + 4). The other options do not correctly factor the expression.

Distribute: 4(3x - 5) + 2

• 12x - 18

• 4x - 5

• 8x - 10

• 12x - 20

Answer explanation

To distribute, multiply 4 by each term in the parentheses: 4 * 3x = 12x and 4 * -5 = -20. Then, add 2: -20 + 2 = -18. The final expression is 12x - 18, which matches the correct answer.

Tags

CCSS.6.EE.A.3

Combine like terms: 5a + 3b - 2a + 4b

• 3a + 4b

• 5a + 7b

• 3a + 7b

• 2a + 5b

Answer explanation

To combine like terms, group the 'a' terms and 'b' terms: (5a - 2a) + (3b + 4b) = 3a + 7b. Thus, the correct answer is 3a + 7b.

Tags

CCSS.7.EE.A.1

Factor: x^2 + 5x + 6

• (x + 3)(x + 5)

• (x + 2)(x + 4)

• (x + 2)(x + 3)

• (x + 1)(x + 6)

Answer explanation

To factor x^2 + 5x + 6, we look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fit this, so the expression factors to (x + 2)(x + 3).