Factor and Remainder Theorem

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 when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

Given the polynomial f(x) = 2x^3 - 3x^2 + 4x - 5, what is the remainder when divided by (x - 1)?

Back

The remainder is -2.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

Front

If f(x) = x^3 - 6x^2 + 3x + 10, which binomial is a factor?

Back

The binomial x + 1 is a factor.

Front

What is the process to find the remainder using synthetic division?

Back

1. Write down the coefficients of the polynomial. 2. Use the value of c from (x - c) to perform synthetic division. 3. The last number obtained is the remainder.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function and influences the degree of the polynomial.

Front

How do you determine if a polynomial is divisible by a binomial?

Back

A polynomial is divisible by a binomial (x - c) if the remainder when divided by (x - c) is 0.

Front

Back

The remainder is 104.

Front

What is the first step in polynomial long division?

Back

Divide the leading term of the dividend by the leading term of the divisor.