What is the leading coefficient of the polynomial f, of, xf(x) defined below?
f, of, x, equals, 9, plus, 6, x, squared, plus, x, to the power 5 , plus, 7, x, cubed, minus, 2, x
f(x)=9+6x
2
+x
5
+7x
3
−2x
Solve the problem just like the example below
⬇️
What is the degree of the polynomial
f, of, x
f(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
1 answer
To find the leading coefficient of the polynomial \( f(x) \) defined as follows:
\[
f(x) = 9 + 6x^2 + x^5 + 7x^3 - 2x
\]
Step 1: Put into standard form
First, we need to rearrange the polynomial in standard form, where the terms are ordered by descending powers of \( x \):
\[
f(x) = x^5 + 7x^3 + 6x^2 - 2x + 9
\]
Step 2: Identify the leading term and the leading coefficient
The leading term is the term with the highest degree, which in this case is \( x^5 \).
Thus, the leading term is:
\[
x^5
\]
The leading coefficient is the coefficient of the leading term, which is \( 1 \).
Step 3: Summary of the results
Leading Term: \( x^5 \)
Leading Coefficient: \( 1 \)
Therefore, the leading coefficient of the polynomial \( f(x) \) is \( \boxed{1} \).
