Math Problem Statement

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

Solution

The polynomial f(x)=8x4+9x3+4x+2f(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 xx. In this case, the highest power of xx is x4x^4, and its coefficient is -8.

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

Would you like further details or have any questions?

Here are five related questions:

  1. What is the degree of the polynomial f(x)=8x4+9x3+4x+2f(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 xx in the expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials

Formulas

Standard form of a polynomial: ax^n + bx^(n-1) + ... + constant term

Theorems

Definition of leading coefficient

Suitable Grade Level

Grades 9-12