The Remainder Factor Theorem and Synthetic Division

Front

What is the Remainder Factor Theorem?

Back

The Remainder Factor Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is 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). It is faster and requires less writing than long division.

Front

How do you set up synthetic division?

Back

To set up synthetic division, write down the coefficients of the polynomial and the zero of the divisor (c) to the left.

Front

What is the first step in synthetic division?

Back

The first step is to bring down the leading coefficient of the polynomial.

Front

What do you do after bringing down the leading coefficient in synthetic division?

Back

Multiply the leading coefficient by the zero of the divisor (c) and write the result under the next coefficient.

Front

What is the purpose of synthetic division?

Back

The purpose of synthetic division is to find the quotient and remainder when dividing polynomials, making calculations easier.

Front

What does the remainder represent in synthetic division?

Back

The remainder represents the value of the polynomial at the zero of the divisor, according to the Remainder Theorem.

Front

If f(x) = 2x^3 + 3x^2 - 5 and you divide by (x - 1), what is the remainder?

Back

The remainder is f(1) = 2(1)^3 + 3(1)^2 - 5 = 2 + 3 - 5 = 0.

Front

What is the quotient in synthetic division?

Back

The quotient is the result of the division, represented by the coefficients obtained after performing synthetic division.

Front

How can synthetic division be used to evaluate polynomials?

Back

Synthetic division can be used to evaluate polynomials at specific values by finding the remainder when divided by (x - c).