Question

Organize the following polynomial expressions from least to greatest based on their degree:

1. x+2xyz
II. 9x³y²
III. 18x²+5ab-6y
IV. 4x⁴+3x²-x-4

a. III, I, IV, II
b. IV, 1, II, III
c. III, II, IV,
d. I IV, III, I, II

Answer 1

To organize polynomial expressions based on their degree from least to greatest, we find the highest exponent in each expression. Upon evaluation, the correct order is Expression III (degree 2), Expression I (degree 3), Expression II (degree 5), and Expression IV (degree 4). Thus, the correct order is Option A: III, I, II, IV.

Step-by-step explanation:

To organize the given polynomial expressions from least to greatest based on their degree, we first identify the degree of each polynomial. The degree of a polynomial is the highest exponent of the variable in any term of the polynomial.

• Expression I (x + 2xyz): The term with the highest degree is 2xyz, which has a degree of 1 (x) + 1 (y) + 1 (z) = 3.
• Expression II (9x³y²): This has a degree of 3 (x³) + 2 (y²) = 5.
• Expression III (18x² + 5ab - 6y): The term with the highest degree is 18x², which has a degree of 2.
• Expression IV (4x⁴ + 3x² - x - 4): The term with the highest degree is 4x⁴, which has a degree of 4.

Now, we can arrange them in order of increasing degree: III, I, II, IV.

The correct answer is Option a: III, I, II, IV, which corresponds to degrees 2, 3, 5, and 4 respectively.