# 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.****If you love our answers, you can login to comment and say hi to us at the comment section…**

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**/ culled from 2020 JAMB-UTME mathematics past question 15 /**