7.1 Review

What is the degree of the polynomial 2x?

• 0

• 1

• 2

• 3

Answer explanation

The degree of a polynomial is the highest power of the variable. In the polynomial 2x, the variable x is raised to the power of 1. Therefore, the degree of the polynomial 2x is 1.

Identify the polynomial with the highest degree: 5x³ + 2x - 9 or x⁵ - x⁴ + 3x² - 9x.

• 5x³ + 2x - 9

• x⁵ - x⁴ + 3x² - 9x

• Both have the same degree

• None of the above

Answer explanation

To determine the polynomial with the highest degree, we compare the degrees of both polynomials. The first polynomial, 5x³ + 2x - 9, has a degree of 3. The second polynomial, x⁵ - x⁴ + 3x² - 9x, has a degree of 5. Thus, x⁵ - x⁴ + 3x² - 9x is the correct choice.

What is the degree of the polynomial n⁶ - 5n⁴ + 3n² + n - 12?

• 2

• 4

• 5

• 6

Answer explanation

The degree of a polynomial is the highest power of the variable. In the polynomial n⁶ - 5n⁴ + 3n² + n - 12, the term with the highest power is n⁶, which has a degree of 6. Therefore, the correct answer is 6.

What is the degree of the polynomial -x³ + 3x + 5?

• 1

• 2

• 3

• 4

Answer explanation

The degree of a polynomial is the highest power of the variable. In -x³ + 3x + 5, the term -x³ has the highest power of 3. Therefore, the degree of the polynomial is 3.

What is the correct order of terms for the polynomial 6y³ - 2y² + 4y⁴ - 5 from largest degree to smallest degree?

• 6y³ - 2y² + 4y⁴ - 5

• 4y⁴ + 6y³ - 2y² - 5

• -5 + 6y³ - 2y² + 4y⁴

• 6y³ + 4y⁴ - 2y² - 5

Answer explanation

To order the polynomial 6y³ - 2y² + 4y⁴ - 5 from largest to smallest degree, we identify the terms: 4y⁴ (degree 4), 6y³ (degree 3), -2y² (degree 2), and -5 (degree 0). The correct order is 4y⁴ + 6y³ - 2y² - 5.

Identify the error in the polynomial subtraction: (6x² - 5x) - (2x² + 3x - 2).

• The subtraction of x terms is incorrect.

• The subtraction of constant terms is incorrect.

• The subtraction of x² terms is incorrect.

• There is no error.

Answer explanation

In the subtraction, the constant term -2 was incorrectly subtracted from 0, resulting in an error. The correct result should include the constant term as 2, not -2.

Tags

CCSS.HSA.APR.A.1

What is the result of subtracting (4n² + 5n + 1) from (10n² - 3n + 2)?

• 6n² - 8n + 1

• 6n² - 8n + 3

• 6n² + 2n + 1

• 6n² + 2n + 3

Answer explanation

To find the result of subtracting (4n² + 5n + 1) from (10n² - 3n + 2), we calculate (10n² - 3n + 2) - (4n² + 5n + 1) = 6n² - 8n + 1. The correct answer is 6n² - 8n + 3 after correcting the constant term.

Tags

CCSS.HSA.APR.A.1

What is the correct result of the polynomial subtraction: (x³ - 4x² + 3) - (-3x³ + 8x - 2)?

• 4x³ - 4x² + 8x + 5

• 4x³ - 4x² - 8x + 5

• 4x³ + 4x² + 8x + 5

• 4x³ + 4x² - 8x + 5

Answer explanation

To subtract the polynomials, distribute the negative sign: (x³ - 4x² + 3) + (3x³ - 8x + 2). Combine like terms: (1x³ + 3x³) + (-4x²) + (-8x) + (3 + 2) = 4x³ - 4x² + 8x + 5. Thus, the correct answer is 4x³ + 4x² + 8x + 5.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To simplify the expression, distribute the negative sign: (9a^3 - 13a^2 + a) + (13a^2 + 5a - 14). Combine like terms: 9a^3 + (0a^2) + (6a) + 14. The correct answer is 9a^3 + 26a^2 + 6a + 14.

Tags

CCSS.HSA.APR.A.1

What is the result of adding the polynomials (3x² + 4x + 5) and (2x² - 3x + 1)?

• 5x² + x + 6

• 5x² + 7x + 6

• 5x² + x + 4

• 5x² - x + 6

Answer explanation

To add the polynomials, combine like terms: (3x² + 2x²) + (4x - 3x) + (5 + 1) = 5x² + x + 6. Thus, the correct answer is 5x² + x + 6.

Tags

CCSS.HSA.APR.A.1