In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highe

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Question: In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highest degree?

Options:

Correct Answer: 2x^4

Solution:

The term with the highest degree in the polynomial k(x) is 2x^4, as it has the highest exponent.

In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highest degree?

In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highest degree?

Step 1: Identify the polynomial given, which is k(x) = 2x^4 - 3x^3 + 0x^2 + 5.
Step 2: Look at each term in the polynomial: 2x^4, -3x^3, 0x^2, and 5.
Step 3: Determine the degree of each term by looking at the exponent of x.
Step 4: The term 2x^4 has an exponent of 4, -3x^3 has an exponent of 3, 0x^2 has an exponent of 2, and 5 has an exponent of 0.
Step 5: Compare the exponents: 4 (from 2x^4), 3 (from -3x^3), 2 (from 0x^2), and 0 (from 5).
Step 6: Identify the highest exponent, which is 4.
Step 7: The term with the highest degree is the one with the highest exponent, which is 2x^4.

Polynomial Degree – Understanding that the degree of a polynomial is determined by the highest exponent of its variable.
Identifying Terms – Recognizing individual terms in a polynomial and their respective coefficients and exponents.