Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

Front

What is the quotient in polynomial division?

Back

The quotient is the result of the division process, representing how many times the divisor can fit into the dividend.

Front

What is the remainder in polynomial division?

Back

The remainder is what is left over after dividing a polynomial by another polynomial when the divisor does not evenly divide the dividend.

Front

How do you find the remainder using the Remainder Theorem?

Back

According to the Remainder Theorem, the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c), using coefficients instead of variables.

Front

What is the first step in polynomial long division?

Back

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

Front

What do you do after finding the first term of the quotient in long division?

Back

Multiply the entire divisor by the first term of the quotient and subtract this from the dividend.

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of a polynomial helps determine the number of times the divisor can fit into the dividend and influences the form of the quotient.

Front

What is the result of dividing a polynomial by a polynomial of a higher degree?

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The result is zero, as the higher degree polynomial cannot divide the lower degree polynomial.

Front

What is the standard form of a polynomial?

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The standard form of a polynomial is expressed as a sum of terms in descending order of their degrees.