What is the leading coefficient of the polynomial f, of, xf(x) defined below?
f, of, x, equals, minus, 8, x, to the power 4 , plus, 9, x, cubed, plus, 4, x, plus, 2
f(x)=−8x 
4
 +9x 
3
 +4x+2

The polynomial \( f(x) = -8x^4 + 9x^3 + 4x + 2 \) is given in standard form.

The **leading coefficient** is the coefficient of the term with the highest power of \( x \). In this case, the highest power of \( x \) is \( x^4 \), and its coefficient is **-8**.

So, the leading coefficient of the polynomial is **-8**.

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Here are five related questions:
1. What is the degree of the polynomial \( f(x) = -8x^4 + 9x^3 + 4x + 2 \)?
2. How do you find the constant term in a polynomial?
3. What is the difference between the degree and the leading coefficient of a polynomial?
4. How do you determine if a polynomial is a monomial, binomial, or trinomial?
5. What is the significance of the leading term in a polynomial for graphing its behavior?

**Tip:** The degree of a polynomial is always the exponent of the highest power of \( x \) in the expression.

What is the leading coefficient of the polynomial f(x) defined below? f(x) = −8x^4 + 9x^3 + 4x + 2

Understand how to find the leading coefficient of the polynomial f(x) = -8x^4 + 9x^3 + 4x + 2. This problem covers key algebraic concepts related to polynomials, suitable for students in Grades 9-12.

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