Answer :
Final answer:
The degree of the polynomial 3x^4 - 9x^2 + 12x^7 - 9x is 7, as the term with the highest exponent is 12x^7 when the polynomial is written in standard form.
Explanation:
The degree of a polynomial is the highest power of the variable present when the polynomial is written in its standard form. In the polynomial 3x^4 - 9x^2 + 12x^7 - 9x, we need to identify the term with the highest exponent to determine the degree of the polynomial.
First, let's rearrange the terms in descending order of their exponents:
12x^7 + 3x^4 - 9x^2 - 9x.
Now, it is clear that the term with the highest power of x is 12x^7, so the degree of this polynomial is 7.
The process for identifying the degree is simple. Remember that coefficients (like the numbers 3, 9, 12, and 9 in this polynomial) do not affect the degree, it's only the exponents of the variable we care about.
