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

If f(c) = 0, then (x - c) is a factor of the polynomial f(x).

Front

What is the remainder when dividing a polynomial by a linear factor?

Back

The remainder is the value of the polynomial evaluated at the root of the linear factor.

Front

If f(x) = x^2 - 5x + 14, what is f(7)?

Back

f(7) = 7^2 - 5(7) + 14 = 49 - 35 + 14 = 28.

Front

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

Back

The remainder is 5.

Front

Calculate the remainder of (3x^3 + 5x - 1) when divided by (x + 1).

Back

The remainder is -9.

Front

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

Back

The remainder is 71.

Front

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

Back

The remainder is -1.

Front

What does it mean if the remainder is zero when dividing a polynomial?

Back

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

Front

How can you find the remainder without performing polynomial long division?

Back

You can use the Remainder Theorem by evaluating the polynomial at the root of the divisor.