Question

What is the degree of the polynomial f, of, xf(x) defined below?
f, of, x, equals, minus, 2, x, to the power 7 , plus, 10, x, to the power 4 , minus, 4, x, to the power 6 , minus, 9, x, cubed, minus, 4, x, to the power 5
f(x)=−2x
7
+10x
4
−4x
6
−9x
3
−4x
5

Put into standard form:
Put into standard form:
f, of, x, equals, minus, 2, x, to the power 7 , minus, 4, x, to the power 6 , minus, 4, x, to the power 5 , plus, 10, x, to the power 4 , minus, 9, x, cubed


Leading Term:
Leading Term:
minus, 2, x, to the power 7
−2x
7

Degree:
Degree:
7
7

Answer 1

To determine the degree of the polynomial \( f(x) \) defined by

\[
f(x) = -2x^7 + 10x^4 - 4x^6 - 9x^3 - 4x^5,
\]

you correctly rearranged it into standard form, which is:

\[
f(x) = -2x^7 - 4x^6 - 4x^5 + 10x^4 - 9x^3.
\]

The degree of a polynomial is defined as the highest power of \( x \) in the polynomial.

In this case, the term with the highest exponent is \( -2x^7 \), where the exponent is \( 7 \).

Therefore, the degree of the polynomial \( f(x) \) is:

**Degree: 7**