7.1 - 7.3 E Learning Quizizz

(4x - 2x³) + (5x³ - 4x + 5)

• 3x³ + 5

• 3x³ + 8x + 5

• 3x² + 5

• 7x³ + 8x + 5

Answer explanation

Combine like terms: (4x - 4x) + (-2x^3 + 5x^3) + 5 = 0 + 3x^3 + 5. Thus, the simplified expression is 3x^3 + 5, which matches the correct answer.

(3 - 2x + 2x²) + (4x - 5 + 3x²)

• 7x - 7x + 5x²

• 5x² + 2x - 2

• 5x²

• 5x² + 6x + 8

Answer explanation

To simplify, combine like terms: (2x^2 + 3x^2) + (-2x + 4x) + (3 - 5) = 5x^2 + 2x - 2. Thus, the correct answer is 5x^2 + 2x - 2.

(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Answer explanation

To simplify (4x² + x) - (x² + 2x), first distribute the negative sign: 4x² + x - x² - 2x. Combine like terms: (4x² - x²) + (x - 2x) = 3x² - x. Thus, the correct answer is 3x² - x.

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Answer explanation

To simplify (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1), combine like terms: 4n^4 - 4n^4 - 8n^2 - 8n + 4 - 1 = -8n^2 - 8n + 3. Thus, the correct answer is -8n^2 - 8n + 3.

(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2

• x + 2

• 2x² + x - 10

• x - 10

Answer explanation

To simplify, distribute the negative sign: (5x + x^2 - 4) - (4x - x^2 + 6) = 5x + x^2 - 4 - 4x + x^2 - 6. Combine like terms: 2x^2 + (5x - 4x) + (-4 - 6) = 2x^2 + x - 10. Thus, the correct answer is 2x^2 + x - 10.

Identify the degree of the monomial:
8a³

• 8

• 1

• 3

• 11

Answer explanation

The degree of a monomial is determined by the sum of the exponents of its variables. In 8a^3, the only variable is 'a' with an exponent of 3. Therefore, the degree of the monomial 8a^3 is 3.

A polynomial that has two terms is a:

• polynomial

• monomial

• binomial

Answer explanation

A polynomial with two terms is specifically called a binomial. In contrast, a monomial has only one term, and a polynomial can have multiple terms. Therefore, the correct answer is binomial.

Classify the polynomial by its degree.
x² + 2x³ - 4

• A
  binomial

• B
  trinomial

• C
  quadratic

• D
  cubic

Answer explanation

The polynomial x^2 + 2x^3 - 4 has a highest degree of 3, which classifies it as a cubic polynomial. Therefore, the correct answer is D, cubic.

Classify the polynomial by its number of terms.
 4x² - 2

• A
  monomial

• B
  binomial

• C
  trinomial

• D
  polynomial

Answer explanation

The polynomial 4x² - 2 has two terms: 4x² and -2. Since it contains exactly two terms, it is classified as a binomial. Therefore, the correct answer is B: binomial.

Which is an example of a cubic monomial?

• A
  x³ + 5

• B
  x² + 3

• C
  x² + 5x - 6

• D
  5x³

Answer explanation

A cubic monomial has the form ax³, where a is a constant. Among the options, D (5x³) is the only one that fits this definition, as it consists of a single term with a degree of 3.