Questions: Give the degree of the polynomial. -8+3 x+3 x^2-3 x^6 The degree of -8+3 x+3 x^2-3 x^6 is .

Give the degree of the polynomial. -8+3 x+3 x^2-3 x^6 The degree of -8+3 x+3 x^2-3 x^6 is .
Transcript text: Give the degree of the polynomial. \[ -8+3 x+3 x^{2}-3 x^{6} \] The degree of $-8+3 x+3 x^{2}-3 x^{6}$ is $\square$.
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Solution

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Solution Steps

To find the degree of a polynomial, identify the term with the highest power of \( x \). The degree is the exponent of that term.

Step 1: Identify the Terms of the Polynomial

The polynomial given is:

\[ -8 + 3x + 3x^2 - 3x^6 \]

Step 2: Determine the Degree of Each Term
  • The constant term \(-8\) has a degree of \(0\).
  • The term \(3x\) has a degree of \(1\).
  • The term \(3x^2\) has a degree of \(2\).
  • The term \(-3x^6\) has a degree of \(6\).
Step 3: Find the Maximum Degree

The degree of the polynomial is the highest degree among its terms. Here, the highest degree is \(6\).

Final Answer

The degree of the polynomial \(-8 + 3x + 3x^2 - 3x^6\) is \(\boxed{6}\).

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