Question

What is the degree of the polynomial f, of, xf(x) defined below?
f, of, x, equals, minus, 4, plus, 6, x, to the power 5 , minus, 2, x, cubed, plus, 2, x, to the power 4 , minus, 10, x, squared

f(x)=−4+6x
5
−2x
3
+2x
4
−10x
2


Solve the problem just like the example below
⬇️
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: 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
f(x)=−2x
7
−4x
6
−4x
5
+10x
4
−9x
3


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

Degree: 7

Answer 1

To find the degree of the polynomial \( f(x) = -4 + 6x^5 - 2x^3 + 2x^4 - 10x^2 \), we will first put it into standard form, where the terms are arranged in descending order of their degrees.

Here are the terms of \( f(x) \):
- \( 6x^5 \)
- \( 2x^4 \)
- \( -2x^3 \)
- \( -10x^2 \)
- \( -4 \)

Putting these into standard form, we have:

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

Now, we identify the leading term. The leading term is the term with the highest degree, which is \( 6x^5 \).

Thus, the leading term is \( 6x^5 \).

To find the degree of the polynomial, we look at the exponent of the leading term:

Degree: \( 5 \)

So, summarizing the answer:

- \( f(x) = 6x^5 + 2x^4 - 2x^3 - 10x^2 - 4 \)
- Leading Term: \( 6x^5 \)
- Degree: \( 5 \)