Problem 17 Identify the terms of each polyn... [FREE SOLUTION]

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Chapter 5: Problem 17

Identify the terms of each polynomial. \(-t^{6}+7 t^{3}-3 t^{2}+6\)

Short Answer

Expert verified

The terms are - t^6, 7 t^3, -3 t^2, and 6.

Step by step solution

- Identify the polynomial

First, observe the expression given: equation: display: oftitle and content: expression

- Break down the polynomial

Identify the different parts of the polynomial, which are separated by '+' or '-' signs: term_1: display_2: 7t^3, term_3: -3t^2, term_4: 6

- List the terms

List all terms identified in the polynomial explicitly: - t^6, 7t^3, -3t^2, 6

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

polynomial identification

Polynomials are algebraic expressions that consist of variables and coefficients. They are composed of terms that are connected by addition or subtraction. Identifying a polynomial involves recognizing the entire structure and understanding its components. When looking at an expression like i.e. t^{6}-7t^{3}+3t^{2}-6, you can determine it is a polynomial by noting the variables raised to whole number powers and their coefficients. Whether it's a single term or several linked by '+' or '-', the key is noticing the variable exponents are non-negative integers.

algebraic expressions

Algebraic expressions are mathematical phrases involving numbers, variables, and operation symbols (like +, -, *, and /). These do not include equality signs as they are not equations. Think of i.e. difference, sums, or products of numbers and variables. In a polynomial, each part of the addition or subtraction is itself an algebraic expression. For instance, 7t^{3}, in the polynomial we studied, is an algebraic expression composed of a constant coefficient and a variable raised to a power. When you combine these parts through addition or subtraction, you construct the full polynomial.

terms in polynomial

Terms in a polynomial are the individual components separated by '+' or '-' signs. Each term is a product of a constant (coefficient) and a variable raised to an exponent. To identify terms, look for the breaks in the expression introduced by addition or subtraction. Let's consider i.e. t^{6}-7t^{3}+3t^{2}-6, The terms here are t^{6}, 7t^{3}, -3t^{2}, and -6. Each term can be isolated and analyzed for its coefficient and the power of the variable. The term '6' is a constant term since it does not contain a variable.

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91影视

Identify the terms of each polynomial. \(-t^{6}+7 t^{3}-3 t^{2}+6\)

Short Answer

Step by step solution

- Identify the polynomial

- Break down the polynomial

- List the terms

Key Concepts

polynomial identification

algebraic expressions

terms in polynomial

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