Polynomial Division

Front

What is Polynomial Division?

Back

Polynomial Division is the process of dividing a polynomial by another polynomial of equal or lower degree, resulting in a quotient and a remainder.

Front

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).

Front

What is Synthetic Division?

Back

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

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 until the degree of the remainder is less than the degree of the divisor.

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 quotient in polynomial division?

Back

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

Front

What is a remainder in polynomial division?

Back

The remainder is what is left over after dividing a polynomial by another polynomial.

Front

What is the relationship between the degree of the dividend and the divisor?

Back

The degree of the quotient will be the degree of the dividend minus the degree of the divisor, provided the degree of the dividend is greater than or equal to that of the divisor.

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.

Front

What does it mean if the remainder is zero in polynomial division?

Back

If the remainder is zero, it means that the divisor is a factor of the dividend.