Factor and Remainder Theorem Flashcard

Front

If 𝑓(𝑥) is a polynomial and (𝑥 - a) is a factor, what is the value of 𝑓(a)?

Back

0

Front

What does the Factor Theorem state?

Back

A polynomial f(x) has a factor (x - a) if and only if f(a) = 0.

Front

What is the Remainder Theorem?

Back

If a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a).

Front

If a polynomial is divided by (x - a) and the remainder is zero, what can you conclude about (x - a)?

Back

It is a factor of the polynomial.

Front

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

Back

5

Front

If 𝑓(𝑥) = 2𝑥^3 - 3𝑥^2 + 4, what is the remainder when 𝑓(𝑥) is divided by (𝑥 - 1)?

Back

3

Front

What is the value of the polynomial 𝑓(𝑥) = 𝑥^2 - 4 at 𝑥 = 2?

Back

0 (since (x - 2) is a factor).

Front

If 𝑓(𝑥) = 𝑥^3 + 2𝑥^2 - 5𝑥 + 6, what is the remainder when divided by (𝑥 - 3)?

Back

0 (since (x - 3) is a factor).

Front

What is the significance of the remainder in polynomial division?

Back

It indicates whether the divisor is a factor of the polynomial.

Front

If a polynomial has a degree of n, what is the maximum number of roots it can have?

Back

n.