Grade 8 Math Exploring Polynomials and Factoring

Answer explanation

To simplify the polynomial 3x + 5x, combine like terms. Adding 3x and 5x gives 8x. Therefore, the simplified form is 8x, which is the correct answer.

Tags

CCSS.7.EE.A.1

Answer explanation

To factor the polynomial x^2 + 5x + 6, we look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 satisfy this, so we can write the polynomial as (x + 2)(x + 3).

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Answer explanation

The degree of a polynomial is the highest power of the variable. In the polynomial 4x^3 - 2x^2 + x - 7, the term with the highest power is 4x^3, which has a degree of 3. Therefore, the correct answer is 3.

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Answer explanation

Substituting x = 2 into the polynomial 2x^2 - 3x + 4 gives 2(2^2) - 3(2) + 4 = 2(4) - 6 + 4 = 8 - 6 + 4 = 6. Therefore, the correct value is 12.

Tags

CCSS.6.EE.A.2C

Answer explanation

The polynomial x^2 - 9 can be factored as (x + 3)(x - 3). Therefore, x + 3 is a factor of the polynomial, making it the correct choice. The other options do not satisfy the factorization.

Tags

CCSS.HSA.APR.B.2

Answer explanation

To simplify \(2(x + 3) + 4(x - 1)\), distribute: \(2x + 6 + 4x - 4\). Combine like terms: \(2x + 4x + 6 - 4 = 6x + 2\). Thus, the correct answer is \(6x + 2\).

Tags

CCSS.6.EE.A.3

Answer explanation

To multiply the polynomials (x + 2) and (x - 3), use the distributive property: x^2 - 3x + 2x - 6. Combine like terms to get x^2 - x - 6, which matches the correct answer.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To factor the polynomial x^2 - 4x, we can factor out the common term x, resulting in x(x - 4). This matches the correct answer choice.

Answer explanation

To find the GCF of 6x^3 and 9x^2, we factor each term. The GCF of the coefficients (6 and 9) is 3, and for the variable part, the lowest power of x is x^2. Thus, the GCF is 3x^2.

Answer explanation

To simplify 5x - 3(x - 2), first distribute -3: 5x - 3x + 6. Then combine like terms: (5x - 3x) + 6 = 2x + 6. Thus, the correct answer is 2x + 6.

Tags

CCSS.6.EE.A.3