Answer :
The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the polynomial function p(x) = 6x⁹ + 4x⁶ + 2x⁴ - 200 has the highest exponent of x as 9.
So, the degree of the polynomial is 9.
A polynomial is an algebraic expression consisting of terms that are formed by multiplying constants and variables raised to non-negative integer exponents.
Each term in a polynomial has a degree, which is the exponent of the variable in that term.
In the polynomial function p(x) = 6x⁹ + 4x⁶ + 2x⁴ - 200, we have four terms:
6x⁹: This term has a degree of 9 because the exponent of x is 9.
4x⁶: This term has a degree of 6 because the exponent of x is 6.
2x⁴: This term has a degree of 4 because the exponent of x is 4.
-200: This term can be thought of as -200x⁰, where x⁰ is always 1. So, its degree is 0.
The degree of a polynomial is determined by the highest exponent among its terms.
In this case, the term with the highest exponent is 6x⁹, which has a degree of 9. Therefore, the degree of the polynomial p(x) is 9.
Thus,
The degree of the polynomial is 9.
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The complete question:
Consider the polynomial function p(x) = 6x⁹ + 4x⁶ + 2x⁴ - 200
what is its degree.
