Question Video: Finding the Remainder Resulting from Dividing Two Given Polynomials | Nagwa Question Video: Finding the Remainder Resulting from Dividing Two Given Polynomials | Nagwa

# Question Video: Finding the Remainder Resulting from Dividing Two Given Polynomials

Given that (π₯ β π) is a factor of π(π₯), what is the remainder when π(π₯) is divided by (π₯ β π)?

01:06

### Video Transcript

Given that π₯ minus π is a factor of π of π₯, what is the remainder when π of π₯ is divided by π₯ minus π?

The factor theorem states that the binomial π₯ minus π is a factor of the polynomial π of π₯ if, and only if, π of π is zero. So if we think of factors, we multiply factors together to equal our polynomial. So letβs simplify this, we can think about it. If we would multiply two and three together, they equal six. So our factors are two and three. Those would be our π₯ minus π examples, and then six would be our polynomial π of π₯. So if we would take our polynomial, which we are representing by six, and dividing it by one of the factors, two or three, what would be our remainder?

We shouldnβt get a remainder because if itβs a factor, that means it goes in there perfectly. So our remainder would be zero.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions