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

13 comments:

  1. but wheres the answer???????????????

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

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

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  4. 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

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  5. what is the answer to question no 10?

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

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  7. What is the answer of question 13 ?

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