Remainder/Factor 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 can you determine if (x - c) is a factor of a polynomial?

Back

If the remainder when dividing the polynomial by (x - c) is zero, then (x - c) is a factor of the polynomial.

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 of the form (x - c).

Front

What is the Factor Theorem?

Back

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

Front

What is the remainder when dividing (x^3 - 5x^2 + 2x - 10) by (x - 5)?

Back

The remainder is 0.

Front

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

Back

The remainder is -1.

Front

What is the remainder when (2x^2 + 10) is divided by (x - 1)?

Back

The remainder is 12.

Front

How do you use synthetic division to show that (x - 5) is a factor of a polynomial?

Back

Perform synthetic division with 5 as the divisor; if the remainder is 0, then (x - 5) is a factor.

Front

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

Back

The remainder is -9.

Front

What is the significance of the remainder in polynomial division?

Back

The remainder provides information about the relationship between the polynomial and its factors; a remainder of 0 indicates a factor.