Question

Class –IX WORKSHEET -II Polynomials Q1. If two polynomials ax3 + 4x2 + 3x – 4 & x3 – 4x + a leave the same remainder when divided by (x – 3), find the value of a. Q2. Evaluate using identities:- (a) 103 x 97 (b) (0.99)2 (c) 1053 Q3. Find the remainder when 4x3—3x2+2x—4 is divided by x+2. Q4. Show that (x – 1) is a factor of x10 – 1 Q5. Find the value of a, if (x – a) is a factor of x3 – a2x + x + 2. Q6. Determine the value of a for which the polynomial 2x4 – ax3 + 4x2 + 2x + 1 is divisible by (1 – 2x). Q7. Factorize x3 – 6x2 + 11x – 6 Q8. Factorize (a2 – b2)3 + (b2 – c2)3 + (c2 – a2)3 Q9. Factorize x3 + 13x2 + 31x – 45 given that x + 9 is a factor Q10. Factorize 8x3 + 273 + z3 – 18xyz Q11. Factorize (a + b)3 + (b + c)3 + (c + a)3 – 3 (a + b) (b + c) (c + a) Q12. Factorize a3 – 0.216 Q13. (x + 1)3 + (x – 1)3 Q14. If p(x) = x2 – 4x+ 3,evaluate p(2) – p(-1) + p(1/2) Q15. Find the dimensions of a cuboid, whose volume is 2py2 + 6py - 20p Q16. If the polynomial ax3 + 3x2 -13 and 2x3 – 5x + a when divided by (x – 2) leave the same remainder, find the Value of a. Q17. Show that x +1 and 2x – 3 are factors of 2x3 – 9x2 + x + 12 Q18. If x – 2 is a factor of a polynomial f(x) = x5 – 3x4 – ax3 + 3ax2 + 2ax + 4, then find the value of a. Q19. Factorize: 4√3x2 + 5x - 2√3 Q20. Factorize: 21x2 – 2x + 1/21

Answer 1

Answer:

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