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 is given in standard form.
The leading coefficient is the coefficient of the term with the highest power of . In this case, the highest power of is , 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:
- What is the degree of the polynomial ?
- How do you find the constant term in a polynomial?
- What is the difference between the degree and the leading coefficient of a polynomial?
- How do you determine if a polynomial is a monomial, binomial, or trinomial?
- 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 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
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