What is the leading coefficient of the polynomial f, of, xf(x) defined below?
f, of, x, equals, minus, 8, x, minus, 10, plus, x, to the power 5 , plus, 3, x, cubed
f(x)=−8x−10+x
5
+3x
3
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:
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:
Leading Term:
minus, 2, x, to the power 7
−2x
7
Degree:
Degree:
7
7
1 answer
To find the leading coefficient of the polynomial \( f(x) = -8x - 10 + x^5 + 3x^3 \), we will first put it into standard form.
Step 1: Put into standard form
The standard form of a polynomial is expressed with the terms arranged in order from the highest degree to the lowest degree.
Rearranging the terms in \( f(x) \):
\[
f(x) = x^5 + 3x^3 - 8x - 10
\]
Step 2: Identify the leading term
The leading term is the term with the highest degree. In this case, the highest degree term is:
\[
x^5
\]
Step 3: Identify the leading coefficient
The leading coefficient is the coefficient of the leading term. In the leading term \( x^5 \), the coefficient is:
\[
1
\]
Conclusion
The leading coefficient of the polynomial \( f(x) = -8x - 10 + x^5 + 3x^3 \) is:
\[
\boxed{1}
\]
