Write each potynomial in standard form. Then, dassify it by degree and by number of terms.

Ask by Allan Lindsey. in the United States

Jan 23,2025

Question

Write each potynomial in standard form. Then, dassify it by degree and by number of terms. $$ \begin{array}{l}	ext { 1. } 4 x+5 x^{2}+8 \ 	ext { 2. } x^{2}-x^{4}+2 x^{2}\end{array} $$

UpStudy AI · Accepted Answer

Sure! Let's go through each polynomial step by step.

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### **1. Polynomial:** $$ 4x + 5x^{2} + 8 $$

#### **a. Standard Form**
To write the polynomial in standard form, arrange the terms in **descending order of degree** (from the highest exponent to the lowest):

$$
5x^{2} + 4x + 8
$$

#### **b. Classification**

- **Degree:** The highest exponent in the polynomial is **2** (from $$5x^{2}$$).  
  **Degree = 2**

- **Number of Terms:** There are **3** terms in the polynomial: $$5x^{2}$$, $$4x$$, and $$8$$.  
  **Number of Terms = 3**

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### **2. Polynomial:** $$ x^{2} - x^{4} + 2x^{2} $$

#### **a. Simplifying and Writing in Standard Form**
First, combine like terms:

$$
x^{2} + 2x^{2} = 3x^{2}
$$

Now, arrange the terms in descending order of degree:

$$
- x^{4} + 3x^{2}
$$

#### **b. Classification**

- **Degree:** The highest exponent in the polynomial is **4** (from $$-x^{4}$$).  
  **Degree = 4**

- **Number of Terms:** There are **2** terms in the polynomial: $$-x^{4}$$ and $$3x^{2}$$.  
  **Number of Terms = 2**

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### **Summary**

| Polynomial           | Standard Form        | Degree | Number of Terms |
|----------------------|-----------------------|--------|-----------------|
| $$4x + 5x^{2} + 8$$  | $$5x^{2} + 4x + 8$$    | 2      | 3               |
| $$x^{2} - x^{4} + 2x^{2}$$ | $$-x^{4} + 3x^{2}$$ | 4      | 2               |

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If you have any more polynomials you'd like to work through or any further questions, feel free to ask!
**Polynomial 1:** - **Standard Form:** $$5x^{2} + 4x + 8$$ - **Degree:** 2 - **Number of Terms:** 3 **Polynomial 2:** - **Standard Form:** $$-x^{4} + 3x^{2}$$ - **Degree:** 4 - **Number of Terms:** 2

Write each potynomial in standard form. Then, dassify it by degree and by number of terms.

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