In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?

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Question: In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?

Options:

Correct Answer: 2x^3

Solution:

The term with the highest degree is 2x^3, as it has the highest exponent of x.

In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?

In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?

Step 1: Identify the polynomial given, which is 2x^3 + 3x^2 - x + 5.
Step 2: Look at each term in the polynomial: 2x^3, 3x^2, -x, and 5.
Step 3: Determine the degree of each term by looking at the exponent of x in each term.
Step 4: The term 2x^3 has an exponent of 3, 3x^2 has an exponent of 2, -x has an exponent of 1, and 5 has no x (exponent of 0).
Step 5: Compare the exponents: 3 (from 2x^3), 2 (from 3x^2), 1 (from -x), and 0 (from 5).
Step 6: Identify the highest exponent, which is 3 from the term 2x^3.
Step 7: Conclude that the term with the highest degree is 2x^3.

Polynomial Degree – Understanding that the degree of a polynomial is determined by the highest exponent of its variable.