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[PDF] CLASS IX MATHEMATICS WORKSHEET CHAPTER 2

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1

CLASS IX

MATHEMATICS WORKSHEET

CHAPTER 2: POLYNOMIALS

VERY SHORT ANSWER TYPE QUESTIONS

Q1. Write an example of an algebraic expression that is not a polynomial. Q2. p(x) = ξݔଷ൅ͳ is not a polynomial. Give reason Q3. Find the value of polynomial 8x3 - 6x2 +2 at x = 1

Q4. If p(x) = 6x3 + 5x2 3x + 2 find p(-1)

Q5. Find the zero of the polynomial p(y) = 2y + 7

Q6. Find the remainder when x101 1 is divided by x -1 Q7. Find whether xn + yn is divisible by x y ( y 0) or not. Q8. Write the following polynomials in standard form i.4y- 4y3 +3 y4 ii.5m3 -6m +7 -2m2 Q9. Write the integral zeroes of the following polynomials i.( x 3) ( x 7 ) ii.( x + 1 ) ( 3x + 2 )

SHORT ANSWER TYPE QUESTIONS

Q10. If y=-1 is a zero of the polynomial q (y) = 4y3 + ky2 - y -1, then find the value of k Q11. For what value of m is x3 2mx2 + 16 divisible by x + 2 Q12. Prove that ( a+ b + c )3 a3 b3 c3 = 3( a+b ) (b + c ) ( c + a )

Q13. If x + 1/x = 5, find the value of x3 + 1/x3

Q14. The polynomials x3 + 2x2 -5ax -7 and x3 + ax2 12x +6 when divided by x + 1 and x 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2 ii. R1 + R2 =0 iii. 2R1 + R2= 0 Q15. If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c 2

Q16. If a+ b + c = 0, prove that :

Q17. Find the zeroes of (x- 2)2 (x+2)2

LONG ANSWER TYPE QUESTIONS

Q18. Factorise p(x) = x4 + x3 7x2 x + 6 by factor theorem Q19. Prove that 2x4 6x3 + 3x2 + 3x 2 is exactly divisible by x2 3x +2 i. By actual division ii. Without actual division Q20. When a polynomial p(x) = x4 2x3 + 3x2 ax + b is divisible by x 1 and x + 1, the remainders are 5 and 19 respectively. Find the remainder when p(x) is divided by x 2. 2

Q21. Simplify:

Q22. If x 3 and x 1/3 are both factors of ax2 + 5x + b , show that a = b

Q23. Factorize:

i. 3(x+2)2 5(x+2)+ 2 ii. x6 + y6 iii. 3ξ͵x3 5ξͷy3

ANSWERS:

3. 4 4.4

5. y=-7/2

6. 0

7. no(show why)

8.i). -y4 - 4y3 + 4y +3

ii). 5m3-2m2 -6m +7

9.i).3, 7 ii).-1

10.4

11.m=1

13.110

14. i). a=-4 ii). a=16/9 iii).a= -11/7

15.1, -1, 2, -3

17.a=5, b=8

18.29

19. (2x + 3y)(3y + 4z)(4z +2x)

22.0

23.i). (3x + 4)(x+1)

ii). (x2 + y2)( x4 +x2y2 + y4) iii). (ξ͵x ξͷy )(3x2 ξͳͷxy +5y2 ) 3quotesdbs_dbs2.pdfusesText_3