Choose the correct classification of 5x + 2. (5 points)

Third degree polynomial

Fourth degree trinomial

First degree binomial

Sixth degree polynomial

2. 

(07.01 MC)

Choose the polynomial written in standard form. (5 points)

xy2 + 4x4y + 10x2

x4y2 + 4x3y + 10x

x4y2 + 4x3y5 + 10x2

x6y2 + 4x3y8 + 10x

3. 

(07.02 LC)

Choose the correct simplification of (4x3 − 3x − 7) + (3x3 + 5x + 3). (5 points)

7x3 − 2x − 4

x3 − 8x − 10

7x3 + 2x − 4

x3 + 8x + 10

4. 

(07.03 LC)

Choose the correct simplification of (5x2y3z4)(6x3y4z2). (5 points)

30x5y7z6

30x6y12z8

11x5y7z6

11x6y12z8

5. 

(07.03 MC)

Choose the correct simplification of (5xy7)2(y2)3. (5 points)

10x2y20

25x2y20

25x2y14

10x2y14

Sure, let's solve these questions one by one:

1. **Choose the correct classification of \(5x + 2\).**
   
   To classify \(5x + 2\), we need to examine its degree and number of terms.
   - The highest exponent of \(x\) is 1, so it is a first-degree polynomial.
   - It has two terms: \(5x\) and 2, making it a binomial.

   **Answer: First degree binomial**

2. **Choose the polynomial written in standard form.**

   The standard form of a polynomial arranges the terms in descending order of the powers of \(x\) (or the main variable).
   - \(xy^2 + 4x^4y + 10x^2\)
   - \(x^4y^2 + 4x^3y + 10x\) 
   - \(x^4y^2 + 4x^3y^5 + 10x^2\)
   - \(x^6y^2 + 4x^3y^8 + 10x\)

   Here, the second option is the polynomial arranged in descending order of powers of \(x\).

   **Answer: \(x^4y^2 + 4x^3y + 10x\)**

3. **Choose the correct simplification of \((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\).**
   
   Combine like terms:
   - \(4x^3 + 3x^3 = 7x^3\)
   - \(-3x + 5x = 2x\)
   - \(-7 + 3 = -4\)

   **Answer: \(7x^3 + 2x - 4\)**

4. **Choose the correct simplification of \((5x^2y^3z^4)(6x^3y^4z^2)\).**
   
   Multiply the coefficients and add the exponents of like bases:
   - Coefficient: \(5 \times 6 = 30\)
   - \(x^{2+3} = x^5\)
   - \(y^{3+4} = y^7\)
   - \(z^{4+2} = z^6\)

   **Answer: \(30x^5y^7z^6\)**

5. **Choose the correct simplification of \((5xy^7)^2(y^2)^3\).**
   
   Simplify each part:
   - \((5xy^7)^2 = 25x^2y^{14}\)
   - \((y^2)^3 = y^6\)

   Combine the results:
   - \(25x^2y^{14+6} = 25x^2y^{20}\)

   **Answer: \(25x^2y^{20}\)**

Would you like more details or have any questions about these solutions?

Here are five additional questions you can ask:
1. How do you classify a polynomial based on its degree and terms?
2. What is the standard form of a polynomial?
3. How do you combine like terms in polynomial addition?
4. What are the rules for multiplying powers with the same base?
5. How do you simplify expressions with exponents?

**Tip:** When simplifying polynomials, always combine like terms by matching variables and their respective exponents.

Explore math problems involving polynomial classification and simplification. Learn how to classify polynomials by degree and terms, and simplify polynomial expressions step-by-step. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation