Addition and Subtraction of Polynomials

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What is a polynomial?
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A polynomial is an expression made up of variables, coefficients, and the operations of addition, subtraction, and multiplication.
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What are the terms in a polynomial?
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Terms in a polynomial are parts of the expression separated by plus or minus signs. Each term contains a coefficient, a variable, and an exponent.
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How do you add polynomials?
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To add polynomials, combine like terms, which are terms with the same variables raised to the same powers.
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How are like terms identified in polynomials?
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Like terms have identical variable letters with the same exponents. Only these can be combined by addition or subtraction.
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What is the result of adding the polynomials 2x + 3 and 4x + 5?
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The sum is 6x + 8.
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How do subtract polynomials?
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To subtract polynomials, distribute the negative sign across the terms of the polynomial being subtracted, then combine like terms.
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What is the opposite of 5x^2 - 3x + 7?
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The opposite is -5x^2 + 3x - 7.
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What happens if you have a negative sign in front of a polynomial?
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You have to distribute the negative sign to each term within the polynomial.
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Subtract the polynomial (3x^2 + 5x + 6) from (7x^2 + 2x - 4). What is the result?
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The result is 4x^2 - 3x - 10.
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What is the role of coefficients in polynomial addition and subtraction?
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Coefficients are the numerical part of the terms, and they're added or subtracted while keeping the variables and exponents unchanged.
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Can you add x^3 + x^2 to 2x? Why or why not?
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No, because they are unlike terms. Terms must have the same variable and power to be added.
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What is the simplified form of 4a + 5a?
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The simplified form is 9a.
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How do you handle parentheses when subtracting polynomials?
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Distribute any negative sign through the parentheses before combining like terms.
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What is the result when you subtract (x^2 + 3x + 1) from (2x^2 - x + 4)?
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The result is x^2 - 4x + 3.
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Why is it important to align terms by degree when adding or subtracting polynomials?
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Aligning terms by degree helps to ensure that only like terms are combined, making simplification easier.
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