Alg 2- Operations of Polynomials

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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. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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What does it mean to add polynomials?

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Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power. The coefficients of these like terms are added together.

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What does it mean to subtract polynomials?

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Subtracting polynomials involves changing the sign of the terms in the polynomial being subtracted and then combining like terms with the first polynomial.

Front

What is the formula for the square of a binomial?

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The square of a binomial (a + b)^2 is given by the formula: a^2 + 2ab + b^2.

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How do you find the product of two binomials?

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To find the product of two binomials, use the distributive property (also known as the FOIL method for binomials): Multiply the first terms, the outer terms, the inner terms, and the last terms, then combine like terms.

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What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 - x + 7, the degree is 3.

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What is a coefficient in a polynomial?

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A coefficient is a numerical factor in a term of a polynomial. For example, in 5x^2, 5 is the coefficient.

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What is a constant term in a polynomial?

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A constant term is a term in a polynomial that does not contain any variables. For example, in the polynomial 3x^2 + 2x + 5, the constant term is 5.

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How do you simplify a polynomial expression?

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To simplify a polynomial expression, combine like terms and arrange the terms in descending order of their degrees.