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Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. 1. 15x4 – 6x + 3x² - 1 II. 12x + 8x + 4 II. 2x5 + 8x2 + 10x Which student's response is correct? 1. Tyler said I and II because the coefficients are decreasing. 2. Susan said only II because all the numbers are decreasing. 3. Fred said II and II because the exponents are decreasing 4. Alyssa said Il and III because they each have three terms.

Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. 1. 15x4 – 6x + 3x² - 1 II. 12x + 8x + 4 II. 2x5 + 8x2 + 10x Which student's response is correct? 1. Tyler said I and II because the coefficients are decreasing. 2. Susan said only II because all the numbers are decreasing. 3. Fred said II and II because the exponents are decreasing 4. Alyssa said Il and III because they each have three terms.

Algebra and Trigonometry (6th Edition)
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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**Polynomial Standard Form Identification** **Context:** Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. **Polynomials:** 1. \( 15x^4 - 6x + 3x^2 - 1 \) 2. \( 12x^3 + 8x + 4 \) 3. \( 2x^5 + 8x^2 + 10x \) **Question:** Which student's response is correct? **Student Responses:** 1. **Tyler:** Said I and II because the coefficients are decreasing. 2. **Susan:** Said only II because all the numbers are decreasing. 3. **Fred:** Said II and III because the exponents are decreasing. 4. **Alyssa:** Said II and III because they each have three terms. **Explanation of Diagrams:** This question does not include any specific graphs or diagrams. The students have different criteria for determining whether the polynomials are in standard form: - Tyler considers the decrease in coefficients. - Susan looks at the overall numbers. - Fred focuses on the order of exponents. - Alyssa notes the number of terms. **Answer Explanation:** In mathematics, a polynomial is in standard form if the terms are written in descending order of their exponents from left to right. 1. \( 15x^4 - 6x + 3x^2 - 1 \) should be rearranged as \( 15x^4 + 3x^2 - 6x - 1 \). 2. \( 12x^3 + 8x + 4 \) is already in standard form. 3. \( 2x^5 + 8x^2 + 10x \) does not need to be rearranged, \( x^2 \) should come before \( x \). Considering this, the correct answer is **Fred said II and III because the exponents are decreasing**.
Transcribed Image Text:**Polynomial Standard Form Identification** **Context:** Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. **Polynomials:** 1. \( 15x^4 - 6x + 3x^2 - 1 \) 2. \( 12x^3 + 8x + 4 \) 3. \( 2x^5 + 8x^2 + 10x \) **Question:** Which student's response is correct? **Student Responses:** 1. **Tyler:** Said I and II because the coefficients are decreasing. 2. **Susan:** Said only II because all the numbers are decreasing. 3. **Fred:** Said II and III because the exponents are decreasing. 4. **Alyssa:** Said II and III because they each have three terms. **Explanation of Diagrams:** This question does not include any specific graphs or diagrams. The students have different criteria for determining whether the polynomials are in standard form: - Tyler considers the decrease in coefficients. - Susan looks at the overall numbers. - Fred focuses on the order of exponents. - Alyssa notes the number of terms. **Answer Explanation:** In mathematics, a polynomial is in standard form if the terms are written in descending order of their exponents from left to right. 1. \( 15x^4 - 6x + 3x^2 - 1 \) should be rearranged as \( 15x^4 + 3x^2 - 6x - 1 \). 2. \( 12x^3 + 8x + 4 \) is already in standard form. 3. \( 2x^5 + 8x^2 + 10x \) does not need to be rearranged, \( x^2 \) should come before \( x \). Considering this, the correct answer is **Fred said II and III because the exponents are decreasing**.
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