# Translating and Solving Polynomial ExpressionsLet's solve the problem step-by-step, focusing on accurately translating the verbal description into mathematical symbols and performing the indicated operations.## Problem Statement**Subtract $ 1.2a^4 - 0.7a $ from the sum of $ 0.6a^4 + 1.5a $ and $ 0.4a^4 - 1.1a $.**## Translation and OperationsFirst, we translate the words of the problem into mathematical symbols.### Identifying Key Phrases- **Subtract from**: This implies a reversal in the order of operations.- **Sum**: This indicates addition.### Step-by-Step SolutionSince $ 1.2a^4 - 0.7a $ is to be subtracted from the sum, the order must be reversed during translation. Here's the detailed translation process:**Step 1: Translate into mathematical symbols**\[ \text{Subtract } 1.2a^4 - 0.7a \text{ from the sum of } 0.6a^4 + 1.5a \text{ and } 0.4a^4 - 1.1a. \]This can be written as:\[ [(0.6a^4 + 1.5a) + (0.4a^4 - 1.1a)] - (1.2a^4 - 0.7a) \]Use brackets $[ ]$ to enclose the sum:\[ [(0.6a^4 + 1.5a) + (0.4a^4 - 1.1a)] - (1.2a^4 - 0.7a) \]**Step 2: Remove the grouping symbols**Combine like terms:\[ 0.6a^4 + 1.5a + 0.4a^4 - 1.1a \]Now, translate:\[ = 0.6a^4 + 1.5a + 0.4a^4 - 1.1a - 1.2a^4 + 0.7a \]**Step 3: Simplify the expression**Combine the $ a^4 $ terms and the $ a $ terms:\[ = (0.6a

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ubtract 1.2a4 - 0.7a from the sum of 0.6 a + 1.5a and 0.4 a4 - 1.1a irst, we will translate the words of the problem into mathematical symbols. Then we will perform the indicated operations. The words of the problem contain the key phrases subtract from and sum. ince 1.2a4 - 0.7a is to be subtracted from the sum, the order must be reversed when we translate to mathematical symbols. ubtract 1.2a4 - 0.7a from the sum of 0.6aª + 1.5a and 0.4a4 - 1.1a. (0.6 aª + 1.5a) + (0.4 a4 – 1.1a)1 – (1.2a4 – 1.7a) Use brackets[ ] to enclose the sum. lext, we remove the grouping symbols to obtain = 0.6 a4 + 1.5a + 0.4 a4 – 1.1a -1.2a4 + 0.7a Change the sign of each term within (1.2a4 – 0.7a) and drop the parentheses. =Daª+ Combine like terms. a ubtract –0.6q² - 0.6q from the sum of 0.1q2 – 0.6q and 0.3q² + 0.1g.

ubtract 1.2a4 - 0.7a from the sum of 0.6 a + 1.5a and 0.4 a4 - 1.1a irst, we will translate the words of the problem into mathematical symbols. Then we will perform the indicated operations. The words of the problem contain the key phrases subtract from and sum. ince 1.2a4 - 0.7a is to be subtracted from the sum, the order must be reversed when we translate to mathematical symbols. ubtract 1.2a4 - 0.7a from the sum of 0.6aª + 1.5a and 0.4a4 - 1.1a. (0.6 aª + 1.5a) + (0.4 a4 – 1.1a)1 – (1.2a4 – 1.7a) Use brackets[ ] to enclose the sum. lext, we remove the grouping symbols to obtain = 0.6 a4 + 1.5a + 0.4 a4 – 1.1a -1.2a4 + 0.7a Change the sign of each term within (1.2a4 – 0.7a) and drop the parentheses. =Daª+ Combine like terms. a ubtract –0.6q² - 0.6q from the sum of 0.1q2 – 0.6q and 0.3q² + 0.1g.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

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

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# Translating and Solving Polynomial Expressions

Let's solve the problem step-by-step, focusing on accurately translating the verbal description into mathematical symbols and performing the indicated operations.

## Problem Statement

**Subtract $ 1.2a^4 - 0.7a $ from the sum of $ 0.6a^4 + 1.5a $ and $ 0.4a^4 - 1.1a $.**

## Translation and Operations

First, we translate the words of the problem into mathematical symbols.

### Identifying Key Phrases

- **Subtract from**: This implies a reversal in the order of operations.
- **Sum**: This indicates addition.

### Step-by-Step Solution

Since $ 1.2a^4 - 0.7a $ is to be subtracted from the sum, the order must be reversed during translation. Here's the detailed translation process:

**Step 1: Translate into mathematical symbols**

\[ \text{Subtract } 1.2a^4 - 0.7a \text{ from the sum of } 0.6a^4 + 1.5a \text{ and } 0.4a^4 - 1.1a. \]

This can be written as:

\[ [(0.6a^4 + 1.5a) + (0.4a^4 - 1.1a)] - (1.2a^4 - 0.7a) \]

Use brackets $[ ]$ to enclose the sum:

\[ [(0.6a^4 + 1.5a) + (0.4a^4 - 1.1a)] - (1.2a^4 - 0.7a) \]

**Step 2: Remove the grouping symbols**

Combine like terms:

\[ 0.6a^4 + 1.5a + 0.4a^4 - 1.1a \]

Now, translate:

\[ = 0.6a^4 + 1.5a + 0.4a^4 - 1.1a - 1.2a^4 + 0.7a \]

**Step 3: Simplify the expression**

Combine the $ a^4 $ terms and the $ a $ terms:

\[ = (0.6a

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