Flashcard - Remainder & Factor Theorem

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What is the Remainder Theorem?

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The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

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How do you find the remainder of a polynomial division?

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To find the remainder of a polynomial f(x) divided by (x - c), evaluate f(c).

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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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.

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What does it mean for a polynomial to be factored?

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Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c).

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree and determines the end behavior of the polynomial function.

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How can you determine if a binomial is a factor of a polynomial?

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To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

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What is the relationship between roots and factors of a polynomial?

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The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial.