Question
What is the degree of x^5+1-3x^4+3x^9-2x
Answers
GPT-4o mini
To find the degree of the polynomial \( x^5 + 1 - 3x^4 + 3x^9 - 2x \), we need to identify the term with the highest exponent of \( x \).
The polynomial can be rewritten with the terms ordered by degree:
\[
3x^9 + x^5 - 3x^4 - 2x + 1
\]
Now, we look for the term with the highest exponent:
- The term \( 3x^9 \) has an exponent of 9.
- The term \( x^5 \) has an exponent of 5.
- The term \( -3x^4 \) has an exponent of 4.
- The term \( -2x \) has an exponent of 1.
- The constant term \( 1 \) has an exponent of 0.
The highest exponent is 9 from the term \( 3x^9 \).
Therefore, the degree of the polynomial \( x^5 + 1 - 3x^4 + 3x^9 - 2x \) is \( \boxed{9} \).
The polynomial can be rewritten with the terms ordered by degree:
\[
3x^9 + x^5 - 3x^4 - 2x + 1
\]
Now, we look for the term with the highest exponent:
- The term \( 3x^9 \) has an exponent of 9.
- The term \( x^5 \) has an exponent of 5.
- The term \( -3x^4 \) has an exponent of 4.
- The term \( -2x \) has an exponent of 1.
- The constant term \( 1 \) has an exponent of 0.
The highest exponent is 9 from the term \( 3x^9 \).
Therefore, the degree of the polynomial \( x^5 + 1 - 3x^4 + 3x^9 - 2x \) is \( \boxed{9} \).