What is the leading coefficient of the polynomial f, of (x) defined below?
f, of, x, equals, x, to the power 4 , minus, 5, x, squared, minus, 10, x, cubed, plus, 6, plus, 10, x
f(x)=x
4
−5x
2
−10x
3
+6+10x
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
1 answer
Let's determine the leading coefficient of the polynomial \( f(x) = x^4 - 10x^3 - 5x^2 + 10x + 6 \).
Step 1: Put into standard form.
The polynomial is already in standard form, ordered by decreasing powers of \( x \):
\[ f(x) = x^4 - 10x^3 - 5x^2 + 10x + 6 \]
Step 2: Identify the leading term.
The leading term is the term with the highest degree. In this case, it is:
\[ x^4 \]
Step 3: Determine the leading coefficient.
The leading coefficient is the coefficient of the leading term. Thus, the leading coefficient of \( f(x) \) is:
\[ 1 \]
Conclusion:
Leading Coefficient: \( 1 \)
Degree: \( 4 \)
