What is the factor Theorem

The video tutorial explains the remainder and factor theorems, starting with an introduction to factors using the number 12. It discusses how factors multiply to give a number and how they evenly divide into it. The concept of divisibility is illustrated using the number 13. The remainder theorem is then explained, showing how it helps determine if a polynomial has a factor by checking if the remainder is zero when divided. The tutorial concludes with methods to prove factors using synthetic or long division.

What is the relationship between the remainder theorem and the factor theorem?

• The remainder theorem is only applicable to even numbers.

• The factor theorem is a subset of the remainder theorem.

• The remainder theorem helps in understanding the factor theorem.

• The remainder theorem is unrelated to the factor theorem.

Which of the following is NOT a factor of 12?

• 3

• 4

• 5

• 6

Why are 13 and 1 the only factors of 13?

• Because 13 is a perfect square.

• Because 13 is a prime number.

• Because 13 is a composite number.

• Because 13 is an even number.

What does a remainder of zero indicate when dividing a polynomial by a binomial?

• The binomial is not a factor.

• The polynomial is prime.

• The binomial is a factor.

• The polynomial is even.

Which method can be used to verify if a binomial is a factor of a polynomial?

• Synthetic division

• Matrix multiplication

• Graphical method

• Substitution method