Polynomial Operations

Flashcard
•
Mathematics
•
9th - 11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
Define a polynomial.
Back
A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.
2.
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 polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.
3.
FLASHCARD QUESTION
Front
What is the leading coefficient of a polynomial?
Back
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in the polynomial 5x^4 + 3x^2 - 2, the leading coefficient is 5.
4.
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 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.
5.
FLASHCARD QUESTION
Front
How do you subtract polynomials?
Back
To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4) - (2x^2 + 5) = (3x^2 - 2x^2) + (4 - 5) = x^2 - 1.
6.
FLASHCARD QUESTION
Front
What is the product of two binomials?
Back
The product of two binomials can be found using the distributive property (FOIL method). For example, (a + b)(c + d) = ac + ad + bc + bd.
7.
FLASHCARD QUESTION
Front
What is the difference of squares?
Back
The difference of squares is a special product that states a^2 - b^2 = (a - b)(a + b). For example, 25 - 16 = (5 - 4)(5 + 4) = 1 * 9 = 9.
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