## Sunday, July 8, 2012

### Polynomials - Class IX

POLYNOMIALS
Practice Questions – Class IX
1.  Find the remainder when x3-ax2+6x-a is divided by x-a.
2.  Find the value of a and b so that the polynomial x3+10x2+ax+b is exactly divisible by (x-1) as well as by (x+2)
3. Find the value of ‘a’ so that x+6 is a factor of x3+3x2+4x+a
4. Show that (x+a) is a factor of xn+an for any odd positive integer n.
5. Find the value of p if (x-p) is a factor of the polynomial x6-px5+x4-px3+3x-p+2.
6. Show that 3 is a zero of the polynomial x3-8x2+8x+21.
7. Prove that x2+2x+3 has no zero.
8. Find the integral zeroes of the polynomial 2x3+5x2-5x-1.
9. Find the values of a and b so that the polynomial x3-ax2-13x+b has (x-1) and (x+3) as factors.
10. If x3+mx2+nx+6 has (x-2) as a factor and leaves remainder 3 , when divided by (x-3) , find the values of m and n.
11. Find the value of p and q so that x-1 and x+1 are factors of x4+px3+2x2-3x+q.
12. Find a & b such that x+2 and x-2 are factors of the polynomials ax4+2x3-3x2+bx-4
13. If x-3 and x-1/3 are both factors of ax2+5x+b, show that a=b
14. Find the value of a3-8b3-36ab-216 when a = 2b+6
15. The polynomials ax3+3x2-3 and 2x3-5x+a when divided by x-4 leaves the remainders p and q respectively. Find the value of a if 2p=q.
16. Prove that (x+y) 3+(y+z) 3+(z+x) 3-3(x+y)(y+z)(z+x)=2(x3+y3+z3-3xyz)
17. Show that x-y , y-z and z-x are factors of x2 (y-z)+y2 (z-x)+z2 (x-y)
18. Find the value of p and q so that x-1 and x+1 are factors of x4+px3+2x2-3x+q.
19. Find a & b such that x+2 and x-2 are factors of the polynomials ax4+2x3-3x2+bx-4
20. If x-3 and x-1/3 are both factors of ax2+5x+b, show that a=b
21. The polynomials ax3+3x2-3 and 2x3-5x+a when divided by x-4 leaves the remainders p and q respectively. Find the value of a if 2p=q.
22. Let A and B be the remainders when polynomials x3+2x2-5ax-7 and x3+ax2-12x+6 are divided by x+1 and x-2 respectively. If 2A+B=6 , find the value of a.
23. Without actually calculating the cubes , evaluate each of the following
a) (-12)3+(7)3+(5)3    b) (18)3+(-13)3+(-5)3       c) (25)3-(75)3+(50)3

1. no answer key?

1. there is no need of answer key

2. there is no need of answer key

3. really nigga?

2. but wheres the answer???????????????

3. if this is the most difficult in polynomial for class 9 i would top in my exams

4. much easy questions

5. if this is the most difficult in polynomial for class 9 i would top in my exams

6. where is the answer key we have done the question but we need to check ,,,,,if u will not give answer please come to my home and check the answer

7. what is the answer to question no 10?

8. what is the answer to question 21 and 22?

9. What is the answer of question 13 ?

10. very easy questions

11. where are the answers?can't you post answer as well.