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

Sure! Let's go through each polynomial step by step. --- ### **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** --- ### **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** --- ### **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 | --- If you have any more polynomials you'd like to work through or any further questions, feel free to ask!