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 determine if (x - c) is a factor of a polynomial?

Back

To determine if (x - c) is a factor of a polynomial f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Front

What is the remainder when (2x^3 - 5x - 7) is divided by (x - 2)?

Back

The remainder is -1.

Front

Is (x - 3) a factor of 3x^3 + 10x^2 - x - 12?

Back

No, it is not a factor.

Front

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

Back

The remainder is 71.

Front

If (x - 7) is not a factor of (x^2 - 5x + 14), what does that imply about the remainder?

Back

It implies that the remainder is not zero.

Front

What is the significance of a non-zero remainder in polynomial division?

Back

A non-zero remainder indicates that the divisor is not a factor of the polynomial.

Front

How can synthetic division be used to find remainders?

Back

Synthetic division is a shortcut method for dividing polynomials that can quickly provide the remainder.

Front

What is the relationship between factors and roots of a polynomial?

Back

If (x - c) is a factor of f(x), then c is a root of the polynomial.

Front

What does it mean if a polynomial has a degree of n?

Back

It means the highest power of the variable in the polynomial is n.