Synthetic Division Review

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). It is faster than long division and is used primarily for polynomials.

Front

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

Back

If the remainder is zero, it indicates that the linear binomial (x - c) is a factor of the polynomial.

Front

How do you determine the remainder when dividing a polynomial by (x - c)?

Back

To find the remainder, substitute c into the polynomial. The result is the remainder.

Front

What is the significance of using a zero placeholder in synthetic division?

Back

A zero placeholder is used to represent missing terms in the polynomial, ensuring that the degrees of the terms align correctly during the division process.

Front

If f(x) = x^3 - 4x + 1, what is f(2)?

Back

f(2) = 2^3 - 4(2) + 1 = 8 - 8 + 1 = 1.

Front

What is the Factor Theorem?

Back

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

Front

What is the relationship between synthetic division and the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of f(x) by (x - c) is f(c). Synthetic division is a method to compute this remainder.

Front

How do you perform synthetic division?

Back

1. Write down the coefficients of the polynomial. 2. Use the root of the divisor (c) on the left. 3. Bring down the leading coefficient. 4. Multiply and add down the columns.

Front

What is the result of dividing x^4 + 3x^2 - 4x - 2 by (x - 2)?

Back

The result is a polynomial of degree 3 with a remainder, which can be found using synthetic division.

Front

What does it mean if (x - 2) is a factor of f(x)?

Back

It means that when f(x) is divided by (x - 2), the remainder is zero.