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: 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 \( f(x) = -8x - 10 + x^5 + 3x^3 \), we will follow these steps:
Put into standard form: We will rearrange the polynomial in order of decreasing powers of \( x \).
Starting with the given polynomial:
\[ f(x) = -8x - 10 + x^5 + 3x^3 \]
We can rearrange it to:
\[ f(x) = x^5 + 3x^3 - 8x - 10 \]
Identify the leading term: The leading term is the term with the highest degree. In this case, the highest degree is \( 5 \), so the leading term is:
\[ x^5 \]
Determine the leading coefficient: The leading coefficient is the coefficient of the leading term. For the leading term \( x^5 \), the coefficient is \( 1 \).
Thus, the leading coefficient of the polynomial \( f(x) \) is:
1
