Polynomial Division Problems

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 of one polynomial by another, representing how many times the divisor fits into the dividend.

Front

What is the remainder in polynomial division?

Back

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

Front

How do you perform polynomial long division?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat the process with the new polynomial until the degree of the remainder is less than the degree of the divisor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor, making calculations quicker and easier.

Front

What is the Factor Theorem?

Back

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

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 the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 5x^2 or -3.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as x + 5 or 3x^2 - 2.