Worksheet on Remainder Theorem

Practice the questions given in the worksheet on Remainder Theorem.


1. Use the Remainder Theorem, find the remainder when 4x\(^{3}\) - 3x\(^{2}\) + 2x - 4 is divided by x + 1.

2. If p(y) = y\(^{3}\) + y\(^{2}\) - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).

3. Find the remainder (without division) when

(a) x\(^{2}\) - 2x + 4 is divided by x - 1

(b) 2x\(^{3}\) - 3x\(^{2}\) + 7x - 8 is divided by x - 1


4. Use the Remainder Theorem, find the remainder when x\(^{4}\) - 3x\(^{2}\) + 4x - 12 is divided by x - 3.



5. Find the remainder (without division) when

(a) x\(^{3}\) + 4x + 2 is divisible by x + 2

(b) 4x\(^{3}\) - 3x\(^{2}\) + 5x + 4 is divided by 2x + 1

(c) 4x\(^{3}\) + 5x\(^{2}\) + 6x - 7 is divided by 2x - 1


6. What number should be added to x\(^{2}\) + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

7. Use the Remainder Theorem, find the remainder when 4x\(^{3}\) - 3x\(^{2}\) + 2x - 4 is divided by x + 1.

8. What number should be subtracted from 3x\(^{2}\) + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

9. Use the Remainder Theorem, find the remainder when x\(^{6}\) + 3x\(^{2}\) + 10 is divided by x - 2.

10.  Find a if the remainder is a when x\(^{3}\) + 3x\(^{2}\) - ax + 3 is divided by x - 2.

11. If the polynomials ax\(^{3}\) + 4x\(^{2}\) + 3x – 4 and x\(^{3}\) - 4x + a leave the same remainder when divided by (x - 3), find the value of a.

12. Find the value of k if the remainder is -3 when kx\(^{3}\) + 8x\(^{2}\) - 4x + 10 is divided by x +1.

13. If both ax\(^{3}\) + 2x\(^{2}\) - 3 and x\(^{2}\) - ax + 4 leave the same remainder when divided by x - 2, find a.


Answers for the worksheet on Remainder Theorem are given below:


Answers:


1. -13

2. 31, a\(^{3}\) + a\(^{2}\) - 2a + 1

3. (a) 3

(b) -2


4. 54

5. (a) -14

(b) \(\frac{1}{4}\)

(c) -\(\frac{9}{4}\)


6. -11

7. -13

8. \(\frac{21}{4}\)

9. 86

10. \(\frac{23}{3}\)

11. a = -1.

12. 25

13. \(\frac{3}{10}\)

 















10th Grade Math

From Worksheet on Remainder Theorem to HOME




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.