9th polynomial test paper

CBSE MATH STUDY 
9th Maths Assignment 
POLYNOMIAL

1. Using factor theorem show x – 2 is a factor of x6 – 64 

2. Factorise using factor theorem2x3 + 7x2 – 9 (ii) 4z3 + 23z2 – 41x – 42 (iii) 6x3 – x2 – 12x – 5 

(iv) 6x2 – 13x + 6 (v) p3(q – r)3 + q3(r – p)3 + r3(p – q)3 

3. Find value using suitable identity 

(a) 9993 (b) 99.83 (c) 703 – 503 - 203

4. Factorize : x3 + y3 + z3 – 3xyz = (x + y + z)[ (x – y)2 + (y – z)2 + (z – x)2 ]

5. Find the remainder when x3 - 5x + 8 is divided by x - 2 

6. Find m if x - 3 is a factor of x3 + x2 – mx + 15

7. Find dimensions of a Cuboid if its volume is 15ax2 + 10ax - 25a 

8. Find value of ‘a’ for which (x – 4) is a factor of (2x 3 – 3x 2 – 18x + a).
9.  Find the constant k if 2 x -1 is a factor of f(x) = 4 x² +kx +1. Using this value of k, factorise f(x) completely.

10. The expression 2 x³ +a x² +bx -2 leaves remainders of 7 and 0 when divided by 2 x -3 and x +2 respectively. Calculate the values of a and b. With these values of a and b, factorise the expression completely.

11. If x +1 and x -1 are factors of f(x) = x³ +2 ax +b, calculate the values of a and b. Using these values of a and b, factorise f(x) completely.

12. If x² -1 is a factor of f(x) = x4 +ax +b, calculate the values of a and b. Using these values of a and b, factories f(x).

13. Given that x² -x -2 is a factor of x³ +3 x² +ax +b, calculate the values of a and b and hence find the remaining factor.

14. The polynomial x4 +bx³ +59 x² +cx +60 is exactly divisible by x² +4 x +3. Find the values of b and c.

15. Show that x -1 is a factor of 2 x² +x -3. Hence factories 2 x² +x -3 completely.

16. Show that 2 x +3 is a factor of 6 x² +5 x -6. Hence find the other factor.
17. Show that x +2 is a factor of f(x) = x³ +2 x² -x -2. Hence Factorise f(x) completely.

18. Show that x -1 is a factor of x5 -1 while x5 +1 is not divisible by x -1.

19. Using remainder theorem, find the value of a if the division of x³ +5 x² -ax +6 by (x -1) leaves the remainder 2

20. find value  of  x3 - 8y3 – 36xy – 216 when x = 2y + 6