Question

Classify by degree: 2x^(2)-x-17 AR.1.3 Which of the following polynomials has the greatest degree A (x-4)(x-3)-x^(2)+4 B (x+3)^(2)-9+x C (x+4)(x-4)-x(x-1)^(2) D (2x-1)^(2)-4x(x-1) Part A Complete th

Answer 1

The polynomial 2x²-x-17 has a degree of 2. After expanding and simplifying each option provided, option C (x+4)(x-4) - x(x-1)² results in a polynomial of degree 3, which is the greatest among the choices.

Step-by-step explanation:

The polynomials provided in the question are classified by their degree, which is the highest power of the variable x that appears in the polynomial. To find the degree, we would expand each expression and identify the term with the highest exponent on x. For the first part of the question, the polynomial 2x²-x-17 has a degree of 2 because the highest power of x is 2. Now, let's classify the degree of each option:

• A. (x-4)(x-3)-x²+4 = x² - 7x + 12 - x² + 4 = -7x + 16 (degree of 1)
• B. (x+3)²-9+x = x² + 6x + 9 - 9 + x = x² + 7x (degree of 2)
• C. (x+4)(x-4) - x(x-1)² = x² - 16 - [x (x² - 2x + 1)] = x² - 16 - x³ + 2x² - x (degree of 3)
• D. (2x-1)² - 4x(x-1) = 4x² - 4x + 1 - 4x² + 4x = 1 (degree of 0)

Comparing the degrees of each polynomial, option C has the greatest degree, which is 3.