Remainder theorem/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

What is the Factor Theorem?

Back

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

Front

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

Back

To find the remainder, evaluate the polynomial at the value that makes the linear factor zero.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c).

Front

When using synthetic division, what number do you use for (x - 2)?

Back

You use 2 for synthetic division with (x - 2).

Front

If f(x) = 2x^3 - 5x^2 + 3x + 7, what is f(2)?

Back

f(2) = 2(2)^3 - 5(2)^2 + 3(2) + 7 = 9.

Front

What is the remainder when a^3 - 4 is divided by a + 2?

Back

The remainder is -12.

Front

How can you determine if (x - 3) is a factor of a polynomial?

Back

Evaluate the polynomial at x = 3. If the result is 0, then (x - 3) is a factor.

Front

What is the result of dividing (2x^3 - 5x^2 + 3x + 7) by (x - 2)?

Back

The result is 2x^2 - x + 1 + 9/(x - 2).

Front

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

Back

The remainder is 5.