Adding and Subtracting Polynomials

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•
Mathematics
•
9th - 12th Grade
•
Hard
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14 questions
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1.
FLASHCARD QUESTION
Front
What is a polynomial?
Back
A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.
2.
FLASHCARD QUESTION
Front
What are like terms?
Back
Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x and -5x are like terms, while 3x and 3x^2 are not.
3.
FLASHCARD QUESTION
Front
How do you add polynomials?
Back
To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.
4.
FLASHCARD QUESTION
Front
How do you subtract polynomials?
Back
To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x + 4) - (2x + 1) = 3x + 4 - 2x - 1 = (3x - 2x) + (4 - 1) = x + 3.
5.
FLASHCARD QUESTION
Front
What is the standard form of a polynomial?
Back
The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 2x^3 + 3x^2 + x + 5 is in standard form.
6.
FLASHCARD QUESTION
Front
What is the degree of a polynomial?
Back
The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 + 5, the degree is 3.
7.
FLASHCARD QUESTION
Front
What is the coefficient in a polynomial?
Back
A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.
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