Find the remainder when x³ – 2x² + 3x – 3 is divided by x² + 1
Find the remainder when x³ – 2x² + 3x – 3 is divided by x² + 1
A. x + 3
B. 2x + 1
C. x – 3
D. 2x – 1
QUICK ANSWER…
D
DETAILS…
Division of this polynomial is done as follows:

The arrangement is done so that the divisor (x² + 1) is at the left-hand side, and what is being divided is the denominator as shown… then the fireworks begins:
We will have to firstly, think of a number such that when we multiply with x² gives x³, its simply x, so, we introduce x at the top so that x multiplied by x² will give x³, the idea is to multiply with x² + 1, and then subtracting the resulting answer from x³ – 2x² + 3x – 3.
So, x × (x² + 1) = x³ + x, that’s written at the fourth line.
So, (x³ – 2x² + 3x – 3) – (x³ + x) will give -2x² + 2x – 3
Now, we need to think of another number such that when multiplied by x² gives -2x², we have it as -2
Now, -2 × (x² + 1) = -2x² – 2
Finally, we have to subtract this (-2x² – 2) from (-2x² + 2x – 3) which gives 2x – 1.
This (2x -1) is the remainder because the power of x here is less than 2.
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is incorrect.
- C is not correct.
- D is the correct answer.
KEY-POINTS…
You may please note these/this:
- The final 2x – 1 is the remainder because the power of x here is less than the power of the divisor which is x² + 1.
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/ culled from 2020 JAMB-UTME mathematics past question 15 /