Question

what is the leading coefficient of the polynomial $f(x)$ defined below? $f(x) = 9x + 4x^3 + x^4 + 5x^2$

Explanation:

Step1: Rearrange the polynomial in standard form (descending powers of x)

To find the leading coefficient, we first write the polynomial in standard form, which is arranging the terms in descending order of their exponents.
Given \( f(x) = 9x + 4x^3 + x^4 + 5x^2 \), when we rearrange the terms by the degree of \( x \) (from highest to lowest), we get:
\( f(x)=x^4 + 4x^3 + 5x^2 + 9x \)

Step2: Identify the leading term and its coefficient

The leading term of a polynomial in standard form is the term with the highest degree. In the polynomial \( f(x)=x^4 + 4x^3 + 5x^2 + 9x \), the term with the highest degree (degree 4) is \( x^4 \).
The coefficient of the leading term (the number multiplied by the variable with the highest degree) is the coefficient of \( x^4 \). For the term \( x^4 \), we can think of it as \( 1\times x^4 \), so the coefficient is 1.

Answer:

1