Polynomials-Sample Questions

Class IX Math
Sample Paper for Polynomials
1.  If x + y = 12 and xy = 32, Find the value of x2 + y2.
2.  If 3x + 2y = 12 and xy = 6, find the value of 9x2 + 4y2.
3.  Write the following cubes in the expanded form:
      (i)   (3a + 4b)3
      (ii)   (5p – 3q)3
4.  If find the values of each of the following:
      (i)   
      (ii)   
5.  If then evaluate
6.  If a + b + c = 15 and a2 + b2 + c2 = 83, find the value of a3 + b3 + c3 – 3abc.
7.  Factorize:
      (i)   6ab – b2 + 12ac – 2bc
      (ii)   9(2a – b)2 – 4(2a – b) – 13
8.  If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2, find the values of a and b.
9.  Using factor theorem, factorize each of the following polynomials:
      (i)   x3 – 6x2 + 3x + 10
      (ii)   2y3 – 5y2 – 19y + 42
10.  Which one is not a polynomial
      (a)   4x2 + 2x – 1
(b)   
(c)   x3 – 1
(d)   y2 + 5y + 1
11.  The number of zeros of x2 + 4x + 2
      (a)   1
(b)   2
(c)   3
(d)   none of these
12.  The value of k, if (x – 1) is a factor of 4x3 + 3x2 – 4x + k, is
      (a)   1
(b)   2
(c)   -3
(d)   3