1018rihannaidn
Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Our experts are ready to provide prompt and detailed answers to any questions you may have.

Select the phrase which contains an error in the verbal description of the given expression:

Consider the expression below.
[tex]\[ \frac{7 x^2(2 x-3)}{3 x^3+4} \][/tex]

The product of seven times the square of [tex]\( x \)[/tex] and the difference of twice [tex]\( x \)[/tex] and three divided by three times the sum of the cube of [tex]\( x \)[/tex] and four.

Sagot :

GinnyAnsweridn
To identify the error in the given verbal description of the algebraic expression [tex]\(\frac{7 x^2(2 x - 3)}{3 x^3 + 4}\)[/tex], let's break down both the verbal description and the mathematical expression step by step.

### Analyzing the Mathematical Expression:
The mathematical expression is:
[tex]\[ \frac{7 x^2(2 x - 3)}{3 x^3 + 4} \][/tex]

### Breaking Down Each Component:
1. Numerator: [tex]\(7 x^2(2 x - 3)\)[/tex]
- [tex]\(7 x^2\)[/tex] means "seven times the square of [tex]\(x\)[/tex]".
- [tex]\((2 x - 3)\)[/tex] is "the difference of twice [tex]\(x\)[/tex] and three".

2. Denominator: [tex]\(3 x^3 + 4\)[/tex]
- [tex]\(3 x^3\)[/tex] means "three times the cube of [tex]\(x\)[/tex]".
- The entire denominator is the expression [tex]\(3 x^3 + 4\)[/tex], which means "the sum of three times the cube of [tex]\(x\)[/tex] and four".

### Verifying the Verbal Description:
The verbal description given is:
"the product of seven times the square of [tex]\(x\)[/tex] and the difference of twice [tex]\(x\)[/tex] and three divided by three times the sum of the cube of [tex]\(x\)[/tex] and four"

### Identifying the Error:
1. Numerator Description:
- "the product of seven times the square of [tex]\(x\)[/tex]"
- "and the difference of twice [tex]\(x\)[/tex] and three"

This part correctly describes [tex]\(7 x^2 (2 x - 3)\)[/tex].

2. Denominator Description:
- "divided by three times the sum of the cube of [tex]\(x\)[/tex] and four"

Let's focus on this part:
- "three times the sum of the cube of [tex]\(x\)[/tex] and four" implies [tex]\(3 \cdot (x^3 + 4)\)[/tex], which suggests that the entire expression [tex]\(x^3 + 4\)[/tex] is multiplied by 3.
- However, the denominator [tex]\(3 x^3 + 4\)[/tex] means [tex]\(3 x^3\)[/tex] (three times the cube of [tex]\(x\)[/tex]) added to 4, not the sum inside a product.

### Conclusion:
The error in the verbal description lies in the phrase:
"three times the sum of the cube of [tex]\(x\)[/tex] and four"
This phrase incorrectly suggests that the entire sum [tex]\(x^3 + 4\)[/tex] is multiplied by 3.

The correct phrase should be:
"the sum of three times the cube of [tex]\(x\)[/tex] and four"

### Final Answer:
The phrase containing an error is:
```
three times the sum of the cube of [tex]\(x\)[/tex] and four
```
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.