Polynomial Factors and Remainder Theorem

The video tutorial explains the relationship between the remainder theorem and the factor theorem. It begins by discussing factors of the number 12 and how they multiply to give the original number. The concept of divisibility is introduced, emphasizing that factors evenly divide a number without a remainder. The remainder theorem is then applied to determine if a polynomial has a factor, using synthetic or long division to check for a remainder of zero. The video concludes by proving factors using the remainder theorem, reinforcing the idea that a remainder of zero indicates a factor.

What does the remainder theorem help us understand?

• The multiplication table

• The factor theorem

• The concept of prime numbers

• The division algorithm

Which of the following is NOT a factor of 12?

• 5

• 3

• 6

• 4

How can the number 12 be broken down using a factor tree?

• 6 * 2

• 5 * 2

• 3 * 3

• 4 * 3

What is a characteristic of a factor of a number?

• It evenly divides the number

• It is always an even number

• It is always a prime number

• It is always greater than the number

What are the only factors of 13?

• 1 and 13

• 1 and 12

• 2 and 13

• 2 and 6

What does a remainder of zero indicate when dividing a number?

• The number is odd

• The divisor is a factor

• The number is even

• The number is prime

According to the remainder theorem, what does a zero remainder signify?

• The number is a prime number

• The number is divisible by 10

• The divisor is a factor

• The divisor is not a factor

What must be true for x-k to be a factor of a polynomial f(x)?

• x-k must be a prime number

• x-k must evenly divide f(x)

• x-k must be greater than f(x)

• x-k must be less than f(x)

Which method can be used to determine if a polynomial has a factor?

• Subtraction

• Addition

• Multiplication

• Synthetic division

What is the result when you plug in the zero of a function and get zero?

• The zero is a prime number

• The zero is a factor

• The zero is not a factor

• The zero is an even number