Factor and Remainder Theorems: Using the Remainder Theorem to Find Remainders in Polynomials

What is the main advantage of using the remainder theorem over algebraic division?

• It is a quicker method to find the remainder.

• It provides the exact quotient.

• It can only be used for quadratic polynomials.

• It eliminates the need for any calculations.

According to the remainder theorem, if a polynomial F(x) is divided by (x - a), what is the remainder?

• F(a)

• x

• a

• 0

In the example where 3X^3 - 10X^2 + X + 8 is divided by X - 3, what value is substituted into the polynomial?

• 0

• 3

• -3

• 8

When using the remainder theorem, what value of X should be chosen to make the bracket (x - a) equal to zero?

• X = -a

• X = 1

• X = 0

• X = a

What is the remainder when 2X^2 + 3X + 6 is divided by X + 4?

• 0

• 26

• 4

• 6

How is the remainder calculated when 6X^3 + 2X^2 + 6 is divided by 2X - 5?

• By using synthetic division

• By substituting X = 5/2 into the polynomial

• By performing long division

• By factoring the polynomial

What is the simplified remainder when 6X^3 + 2X^2 + 6 is divided by 2X - 5?

• 112.25

• 449

• 5

• 0