Dividing Polynomials

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor, allowing for quicker calculations.

Front

How do you determine if (x - c) is a factor of a polynomial?

Back

Use the Factor Theorem: If f(c) = 0, then (x - c) is a factor of the polynomial f(x).

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

How do you find the quotient in polynomial division?

Back

To find the quotient, divide the leading term of the dividend by the leading term of the divisor, then multiply the entire divisor by this result and subtract from the dividend.

Front

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

Back

The leading coefficient affects the end behavior of the polynomial and is crucial in determining the quotient during division.

Front

What is a remainder in polynomial division?

Back

The remainder is what is left over after dividing a polynomial by another polynomial when the division is not exact.

Front

How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial in descending order and use the zero of the divisor (x - c) as the value for synthetic division.

Front

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

Back

The remainder is -1.