Division and Solving Polynomials Flashcard Review

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

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How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial in descending order, and place the zero of the divisor (x - c) to the left.

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What is the remainder theorem?

Back

The remainder theorem states that when a polynomial f(x) is divided by (x - c), the remainder 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 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 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.

Front

What does it mean for a polynomial to be in standard form?

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A polynomial is in standard form when its terms are arranged in descending order of their degrees.

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What is the process for dividing polynomials using long division?

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1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by the result and subtract from the dividend. 3. Repeat the process with the new polynomial until the degree of the remainder is less than the degree of the divisor.

Front

What is the result of dividing a polynomial by a linear factor?

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The result is a polynomial of one degree less than the original polynomial, plus a remainder.