Question
what degree is this 6x^6+9x^3+3x^2-4x^10-9x^5-5x^6
Answers
GPT-4o mini
To determine the degree of the polynomial \( 6x^6 + 9x^3 + 3x^2 - 4x^{10} - 9x^5 - 5x^6 \), we first combine like terms and simplify the expression.
1. Combine the \( x^6 \) terms:
\[
6x^6 - 5x^6 = 1x^6
\]
2. The polynomial now looks like:
\[
-4x^{10} + 1x^6 - 9x^5 + 9x^3 + 3x^2
\]
3. The degree of a polynomial is defined as the highest power of \( x \) that appears in the polynomial.
In this case, the highest power is \( x^{10} \) from the term \( -4x^{10} \).
Therefore, the degree of the polynomial is \( \boxed{10} \).
1. Combine the \( x^6 \) terms:
\[
6x^6 - 5x^6 = 1x^6
\]
2. The polynomial now looks like:
\[
-4x^{10} + 1x^6 - 9x^5 + 9x^3 + 3x^2
\]
3. The degree of a polynomial is defined as the highest power of \( x \) that appears in the polynomial.
In this case, the highest power is \( x^{10} \) from the term \( -4x^{10} \).
Therefore, the degree of the polynomial is \( \boxed{10} \).