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 equal or lower degree, similar to long division with numbers.

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 do you do after finding the first term in polynomial long division?

Back

Multiply the entire divisor by the term found and subtract the result from the dividend.

Front

What is a remainder in polynomial division?

Back

A remainder is the part of the dividend that is left over after division when the divisor does not evenly divide the dividend.

Front

How do you find the remainder when dividing polynomials?

Back

You can find the remainder by performing polynomial long division or by using the Remainder Theorem.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that 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 form of polynomial long division that is used when dividing by a linear factor.

Front

When can you use synthetic division?

Back

You can use synthetic division when dividing a polynomial by a linear polynomial of the form (x - c).

Front

What is the result of dividing (x^3 - 125) by (x - 5)?

Back

The result is x^2 + 5x + 25.

Front

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

Back

The leading coefficient helps determine the degree of the quotient and the behavior of the polynomial as x approaches infinity.