What is the remainder when (x3 + 1) is divided by (x2 – x + 1)?
Answer: The remainder is zero when (x3 + 1) is divided by (x2 – x + 1).
Let us see how we will use the long division method.
Using long division method: (x3 + 1) ÷ (x2 - x + 1)
Multiply (x2 - x + 1) by x and subtract from ( x3 + 1 )
= (x3 + 1) - (x2 - x + 1) × (x)
= x3 + 1 - x3 + x2 - x
= x2 - x + 1
Multiply (x2 - x + 1) by 1 and subtract from the remainder in first step.
= (x2 - x + 1) - (x2 - x + 1 )
There is no remainder left. That means (x3 + 1) is completetly divisible by (x2 - x + 1)
You can see the image, how long division is performed:
Cuemath's online calculator helps you divide large polynomials and finds the quotient and the remainder