Remainder theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).

Front

How do you find the remainder of a polynomial when divided by a linear factor?

Back

To find the remainder of a polynomial f(x) when divided by (x - c), evaluate f(c).

Front

What is the remainder when (3x^3 - 5x^2 - 4x + 1) is divided by (x + 3)?

Back

-113

Front

If (x - 2) is not a factor of (2x^3 - 5x - 7), what is the remainder?

Back

-1

Front

What is the remainder when (x^2 + 3x + 7) is divided by (x + 2)?

Back

5

Front

If (2x^2 + 10) is divided by (x - 1), what is the remainder?

Back

12

Front

What does it mean if a polynomial has a remainder of 0 when divided by a linear factor?

Back

It means that the linear factor is a factor of the polynomial.

Front

How can you verify the Remainder Theorem using synthetic division?

Back

You can use synthetic division to divide the polynomial by (x - c) and the final value will be the remainder.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used specifically for dividing by linear factors.

Front

What is the relationship between factors and remainders in polynomial division?

Back

If a polynomial f(x) is divided by (x - c) and the remainder is 0, then (x - c) is a factor of f(x).