교과서 질문
Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. 9
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Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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1장, 문제 23
Add or subtract, as indicated.
검증된 단계별 안내1
Identify the polynomials to be added: \((5x^2 - 4x + 7)\) and \((-4x^2 + 3x - 5)\).
Remove the parentheses and write the expression as a sum of all terms: \(5x^2 - 4x + 7 - 4x^2 + 3x - 5\).
Group like terms together. Like terms have the same variable raised to the same power: \((5x^2 - 4x^2) + (-4x + 3x) + (7 - 5)\).
Combine the coefficients of each group: For \(x^2\) terms, add \(5\) and \(-4\); for \(x\) terms, add \(-4\) and \(3\); for constants, add \(7\) and \(-5\).
Write the simplified polynomial by combining the results from the previous step, keeping the variable parts intact.
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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Polynomial Addition and Subtraction
Adding or subtracting polynomials involves combining like terms, which are terms with the same variable raised to the same power. You add or subtract their coefficients while keeping the variable part unchanged. This process simplifies the expression into a single polynomial.
추천 영상:
가이드 코스
03:34
Adding and Subtracting Polynomials
Like Terms
Like terms are terms in a polynomial that have identical variable parts, including the same exponents. For example, 5x² and -4x² are like terms because both have x raised to the second power. Recognizing like terms is essential for correctly combining polynomials.
추천 영상:
가이드 코스
03:50Adding & Subtracting Like Radicals
Distributive Property
The distributive property allows you to multiply a term outside parentheses by each term inside. When subtracting polynomials, you distribute the negative sign across all terms in the second polynomial before combining like terms. This ensures correct addition or subtraction of coefficients.
추천 영상:
가이드 코스
04:15Multiply Polynomials Using the Distributive Property
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