1) Find the zeros of the polynomial (a) x2 + 7x + 10 (b) x2 – 25
2) Using factor theorem, Show that (a -
b) is the factor of a (b2-c2)
+b (c2-a2) +c (a2-b2)
3) Factorize: (a) 4√3x2 + 5x - 2√3 (b)
21x2 – 2x + 1/21 (c) 9(2a – b)2 – 4(2a – b) –13
4) Factorize: a) 9992 - 1 b) (10.2)3 c) 1002 X 998
5) Factorize: a) x3 – 3x2
– 9x – 5 b) x3 + 7x2 – 21x – 27
6)
Factorise: (a) 3x2 + 27y2 + z2 - 18xy +6 √3yz
-2 √3zx (b) 27 x3 + 125y3 ( c) (2a – 3b + c )2
(d) [x
– 1/x y]3 (e) x4 y4 – x y
(f) 8x3 – (2x – y)3 (g) 27 a6 - 1
7)
For what value of a is 2x3 + ax2 + 11x + a + 3 exactly
divisible by (2x – 1)
8) If x – 2 is a factor of a
polynomial f(x) = x5 – 3x4 – ax3 + 3ax2
+ 2ax +4, then find the value of a
9) Find the value of a and b so
that x2 – 4 is a factor of ax4 + 2x3 – 3x2
+ b x – 4
10) Find the value of a and b so
that polynomial x3 – ax2 -13x + b is exactly divisible by
(x-1) as well as (x+3)
11)
The polynomial x3 – mx2 +4x + 6 when
divided by (x+2) leaves remainder 14 find the value of m
12) If the polynomial ax3
+ 3x2 -13 and 2x3 – 5x + a when divided by (x – 2) leave
the same remainder, find the Value of “a”
13) If both (x – 2) and (x – ½) are
factors of px2 + 5x + r, show that p = r
14) If f(x) = x4 – 2x3
+ 3x2 – ax + b is divided by x-1 and x+1 the remainders are 5 and 19
respectively, then find a and b
15) Show that x + 1 and 2x – 3 are
factors of 2x3 – 9x2 + x + 12
16) By using suitable identity,
find the value of:
(a) (-6)3 + 133+ (-7)3 (b)
(-21)3 + (28)3 (c)
(9.8)3 – (11.3)3 + (1.5)3 (d) (8/15)3 + (-1/3)3 +
(-1/5)3
17) Find the remainder when f(x) =
4x3 – 12x2 + 14x – 3 is divided by g(x) = x – 1
18) Find the remainder when x51
+ 51 is divided by x + 1
20) Find the remainder when x3
– px2 + 6x – p is divided by (x–p)
21) Find the value of x3
+ y3 + 15xy – 125 when x + y = 5
22) Find the value of p3
– q3 , if p – q = 5/7 and p q
= 7/3
23)
If a + b + c =8, a2 + b2 + c2 = 30. Find the
value of a b + b c + c a
24)
If 2x + 3y = 13 and x y = 6 then, find 8x3 + 27y3
25) Find
the value of a3+b3+c3–3abc,
when a+b+c=8 and ab+bc+ca=25
26) Find the value of x3
+ y3 + z3 – 3xyz, if x+y+z = 12 and x2 + y2
+ z2 =70
27) If x + y + z = 1, x y + y z + z
x = -1 and xyz = -1, find the value of x3 + y3 +z3
28)
If (a + b)2 = 2a2 + 2b2, show that a = b
29) If (a + b + c) = 0, then prove
that a3 + b3 + c3 = 3abc
30) Prove that 2x3 +2y3
+ 2z3 – 6xyz =(x + y + z) [(x – y )2 + ( y – z )2
+ ( z – x )2 ]
31)
Give possible expressions for the length and breadth of each of the following
rectangles, in which their areas are given
25a2 – 35a + 12
32)Simplify
: (a + b + c )2 + (a – b + c )2 + ( a + b - c)2
33)What
must be subtracted from 4x4 – 2x3 – 6x2 + x –
5, so that the result is exactly divisible
by 2x2 + x
- 1
34)Find the dimensions of a cuboid,
whose volume is 2py2 + 6py - 20p
35)
If p(x) = x2 – 4x + 3, evaluate p (2) – p (-1) + p (1/2)
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