A2 - 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 is f(c).

Front

How do you perform synthetic division?

Back

Synthetic division is a simplified form of polynomial long division. It involves using the coefficients of the polynomial and the zero of the divisor.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

If f(x) = 2x^3 + 3x^2 - 5, what is f(1)?

Back

f(1) = 2(1)^3 + 3(1)^2 - 5 = 0.

Front

What does it mean for (x - 3) to be a factor of a polynomial?

Back

It means that when the polynomial is divided by (x - 3), the remainder is zero.

Front

How can you find all factors of a polynomial?

Back

You can find all factors by using synthetic division, the Factor Theorem, and testing possible rational roots.

Front

What is the significance of finding zeros of a polynomial?

Back

Finding zeros helps in graphing the polynomial and understanding its behavior.

Front

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

Back

The result is 2x^2 - x + 1 with a remainder of 9.

Front

If f(-2) = 0, what does this imply about the polynomial f(x)?

Back

It implies that (x + 2) is a factor of f(x).