Worksheet: Polynomial Remainder Theorem: Checking Factors of Polynomials

In this worksheet, we will practice checking if a given binomial is a factor of f(x) by using synthetic division.

Q1:

A polynomial 𝑓 ( 𝑥 ) is divided by ( 𝑥 𝑎 ) . Given that ( 𝑥 𝑎 ) is not a factor of 𝑓 ( 𝑥 ) , what is the remainder equal to?

  • A0
  • B 𝑓 ( 𝑥 )
  • C 𝑓 ( 𝑟 )
  • D 𝑓 ( 𝑎 )

Q2:

Given that ( 𝑥 𝑎 ) is a factor of 𝑓 ( 𝑥 ) , what is the remainder when 𝑓 ( 𝑥 ) is divided by ( 𝑥 𝑎 ) ?

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