Determine the leading term, the leading coefficient, and the degree of the polynomial.
Then classify the polynomial as constant, linear, quadratic, cubic, or quartic.

Ask by Curry Potter. in the United States

Mar 20,2025

Question

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. $$ h(x)=-6 x+5 x^{2}+x^{3} $$

UpStudy AI · Accepted Answer

**Step 1: Write the Polynomial in Standard Form**

The given polynomial is  
$$
h(x) = -6x + 5x^2 + x^3.
$$  
Rewriting it in descending order of exponents, we get:  
$$
h(x) = x^3 + 5x^2 - 6x.
$$

**Step 2: Identify the Leading Term and Leading Coefficient**

The leading term is the term with the highest power of $$x$$. In this polynomial, the highest power is $$x^3$$.  
- **Leading Term:** $$x^3$$  
- **Leading Coefficient:** The coefficient of $$x^3$$ is $$1$$.

**Step 3: Determine the Degree of the Polynomial**

The degree of a polynomial is the highest exponent on $$x$$. Here, the highest exponent is $$3$$.  
- **Degree:** $$3$$

**Step 4: Classify the Polynomial**

A polynomial of degree $$3$$ is classified as a **cubic** polynomial.

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**Summary:**  
- **Leading Term:** $$x^3$$  
- **Leading Coefficient:** $$1$$  
- **Degree:** $$3$$  
- **Classification:** Cubic polynomial.
**Leading Term:** $$x^3$$ **Leading Coefficient:** $$1$$ **Degree:** $$3$$ **Classification:** Cubic polynomial

Determine the leading term, the leading coefficient, and the degree of the polynomial.
Then classify the polynomial as constant, linear, quadratic, cubic, or quartic.

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