Long Division Polynomials

Front

What is long division of polynomials?

Back

Long division of polynomials is a method used to divide a polynomial by another polynomial of lower degree, similar to numerical long division.

Front

What is the first step in long division of polynomials?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

Front

How do you find the remainder in polynomial division?

Back

The remainder can be found by evaluating the polynomial at the root of the divisor or by using the division algorithm.

Front

What is the division algorithm for polynomials?

Back

The division algorithm states that for any polynomials f(x) and g(x) (where g(x) is not zero), there exist unique polynomials q(x) and r(x) such that f(x) = g(x) * q(x) + r(x), where the degree of r(x) is less than the degree of g(x).

Front

What is the result of dividing (2x^3 - 5x^2 + 3x + 7) by (x - 2)?

Back

The result is 2x^2 - x + 1 + 9/(x - 2).

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What is the remainder when dividing (x^2 + 5x - 8) by (x + 3)?

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The remainder is -14.

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What does it mean if a polynomial division is incorrect?

Back

It means that the steps taken in the division process did not yield the correct quotient or remainder, indicating a mistake in calculation.

Front

What is the purpose of polynomial long division?

Back

The purpose is to simplify the division of polynomials to find the quotient and remainder, which can be useful in solving polynomial equations.

Front

What is the leading term of a polynomial?

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The leading term is the term in a polynomial that has the highest degree.