Factor and Remainder Theorem

Front

What is the Factor Theorem?

Back

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

Front

What is the Remainder Theorem?

Back

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

Front

How do you find the real zeros of a polynomial function?

Back

To find the real zeros of a polynomial function, set the function equal to zero and solve for x.

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

If f(x) = 2x^3 - 19x^2 + 38x + 24 and (x - 4) is a factor, what are the real zeros?

Back

The real zeros are x = 4, -1/2, and 6.

Front

How do you use synthetic division to evaluate f(5) for f(x) = 3x^2 - 9x - 20?

Back

Use synthetic division with 5 to find f(5) = 10.

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

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

Back

No, (x - 3) is not a factor.

Front

What is the first step in using synthetic division?

Back

The first step is to write down the coefficients of the polynomial.

Front

What does it mean if f(c) = 0 for a polynomial f(x)?

Back

It means that (x - c) is a factor of the polynomial.