I need help with all of them plz. # Understanding PolynomialsIn this section, we will learn how to describe and analyze polynomials by identifying their variables, the number of terms, and their degrees. We will also determine if the polynomials are written in ascending or descending order.## Definition and Identification**Polynomial**: A mathematical expression consisting of variables, coefficients, and exponents. Example: $x^3 - 4x^2 + 7$.### Key Concepts:- **Term**: A single part of a polynomial, e.g., $x^3$ in $x^3 - 4x^2 + 7$.- **Coefficient**: The numerical factor in a term, e.g., 3 in $3x^2$.- **Degree of a Term**: The exponent of the variable, e.g., the degree of $x^3$ is 3.- **Degree of the Polynomial**: The highest degree of any term in the polynomial.## Example PolynomialsLet's analyze the given polynomials:### Polynomial (a)**Expression**: $d^4 + 9d^2 - 16$1. Identify the number of terms: - $d^4$ - $9d^2$ - $-16$2. Variables and Degrees: - The term $d^4$ has a degree of 4. - The term $9d^2$ has a degree of 2. - The constant term $-16$ has a degree of 0.**Table Representation**:| Term | Coefficient | Degree ||--------|-------------|--------|| $d^4$ | 1 | 4 || $9d^2$ | 9 | 2 || $-16$ | -16 | 0 |**Conclusion:**- This is a trinomial (3 terms).- The highest degree is 4.- The polynomial is of degree 4.---### Polynomial (b)**Expression**: $\frac{1}{2}x^2 - x$1. Identify the number of terms: - $\frac{1}{2}x^2$ - $-x$2. Variables and Degrees: - The term $\frac{1 ### Polynomial Identification and Degree Evaluation#### Instructions:For each polynomial provided below, identify whether it is a monomial, binomial, or trinomial by using the dropdown list. Then, state the degree of the polynomial by filling in the appropriate box.### Problem (a)- Polynomial: \( x^5 + 6x - 36 $ - **Dropdown Menu:** binomial (currently selected) - **Degree Box:** (empty)### Problem (b)- Polynomial: $ -15s^4t + s^3t^3 $ - **Dropdown Menu:** monomial (currently selected) - **Degree Box:** (empty)#### Explanation of Terms:1. **Monomial:** A polynomial consisting of only one term. Examples include $ 5x $, $ -3 $, or $ 7t^2 $.2. **Binomial:** A polynomial consisting of exactly two terms. Examples include $ x + 1 $ or $ 4x^2 - 9 $.3. **Trinomial:** A polynomial consisting of exactly three terms. Examples include $ x^2 + x + 1 $ or $ 3x^3 - 2x + 5 $.4. **Degree of Polynomial:** The highest power of the variable in the polynomial. For example, the degree of $ x^5 + 6x - 36 $ is 5 because the term with the highest power is $ x^5 $.Please ensure to select the correct polynomial type from the dropdown menu and fill in the correct degree for each polynomial.

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Answered: Describe each polynomial. „(a)..x...6x.…

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Describe each polynomial. „(a)..x...6x. 36 of degree binomial (b) –15s“t + s³3 monomial v of degree -

Algebra and Trigonometry (6th Edition)

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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I need help with all of them plz.

# Understanding Polynomials

In this section, we will learn how to describe and analyze polynomials by identifying their variables, the number of terms, and their degrees. We will also determine if the polynomials are written in ascending or descending order.

## Definition and Identification

**Polynomial**: A mathematical expression consisting of variables, coefficients, and exponents. Example: $x^3 - 4x^2 + 7$.

### Key Concepts:

- **Term**: A single part of a polynomial, e.g., $x^3$ in $x^3 - 4x^2 + 7$.
- **Coefficient**: The numerical factor in a term, e.g., 3 in $3x^2$.
- **Degree of a Term**: The exponent of the variable, e.g., the degree of $x^3$ is 3.
- **Degree of the Polynomial**: The highest degree of any term in the polynomial.

## Example Polynomials

Let's analyze the given polynomials:

### Polynomial (a)
**Expression**: $d^4 + 9d^2 - 16$

1. Identify the number of terms:
- $d^4$
- $9d^2$
- $-16$

2. Variables and Degrees:
- The term $d^4$ has a degree of 4.
- The term $9d^2$ has a degree of 2.
- The constant term $-16$ has a degree of 0.

**Table Representation**:

| Term | Coefficient | Degree |
|--------|-------------|--------|
| $d^4$ | 1 | 4 |
| $9d^2$ | 9 | 2 |
| $-16$ | -16 | 0 |

**Conclusion:**
- This is a trinomial (3 terms).
- The highest degree is 4.
- The polynomial is of degree 4.

---

### Polynomial (b)
**Expression**: $\frac{1}{2}x^2 - x$

1. Identify the number of terms:
- $\frac{1}{2}x^2$
- $-x$

2. Variables and Degrees:
- The term \(\frac{1

### Polynomial Identification and Degree Evaluation

#### Instructions:
For each polynomial provided below, identify whether it is a monomial, binomial, or trinomial by using the dropdown list. Then, state the degree of the polynomial by filling in the appropriate box.

### Problem (a)
- Polynomial: $ x^5 + 6x - 36 $
- **Dropdown Menu:** binomial (currently selected)
- **Degree Box:** (empty)

### Problem (b)
- Polynomial: $ -15s^4t + s^3t^3 $
- **Dropdown Menu:** monomial (currently selected)
- **Degree Box:** (empty)

#### Explanation of Terms:
1. **Monomial:** A polynomial consisting of only one term. Examples include $ 5x $, $ -3 $, or $ 7t^2 $.
2. **Binomial:** A polynomial consisting of exactly two terms. Examples include $ x + 1 $ or $ 4x^2 - 9 $.
3. **Trinomial:** A polynomial consisting of exactly three terms. Examples include $ x^2 + x + 1 $ or $ 3x^3 - 2x + 5 $.
4. **Degree of Polynomial:** The highest power of the variable in the polynomial. For example, the degree of $ x^5 + 6x - 36 $ is 5 because the term with the highest power is $ x^5 $.

Please ensure to select the correct polynomial type from the dropdown menu and fill in the correct degree for each polynomial.

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