Holidays Home Work ( Class - IX )

MATHEMATICS

1)      Find the zeros of the following polynomials

i)        2x³ + 3x² – 11x – 6

ii)       2x³ + x² – 2x – 1

2)      Use long division to find the remainder, when  4x³ - 12 x² + 14x – 3 is divided by 2x – 1. Also verify the result by remainder theorem

3)      If ( 4x + 2 ) is a factor of  4x³ – kx² + 56x – 24, find the value of k

4)      If the polynomials ax³ – 3x² – 13and 2x³ – 5x² +a, leave the same remainder when divided by x – 2. Find the value of a and also the remainder in each case

5)      Show that (x +2 ), ( x – 5 ) and ( x + 9 ) are the factors of 

x³ + 6x² – 37x – 90

6)      What must be subtracted from  4x⁴ – 2x³ – 6x² + x – 5 so that the result is exactly divisible by 2x² + x – 1

7)      Find the product 

i)        ( x³ – 6x² – x ) ( x² – 6x + 1 )

ii)       ( 1.5x² – 0.3y² ) ( 1.5x² + 0.3y² )

iii)      ( x³ + 1 )( x⁶ – x³ + 1 )

iv)      ( a² – b² + c² )( a⁴ + b⁴ + c⁴ + a²b² + b²c² – c²a²)

v)       ( 2x – y + 3z )( 4x² + y² + 9z² + 2xy  + 3yz – 6zx )

8)      Evaluate

i)         ( 25 )³ – ( 75 )³ + ( 50 )³

ii)        ( 0.2 )³ – ( 0.3 )³ + ( 0.1 )³

iii)      ( 1002 )³

iv)     29³ – 11³

v)      46³ + 34³

9)      If a + b = 100 and a² + b² = 436, find the value of a³ + b³

10)   If a – b = 40 and ab = 600, find the value of a² + b² +ab

11)   If a + b+ c = 9 and a² – b² + c² = 83, then find the value of a³ + b³ + c³ – 3abc

1)      Factorise

i)        a² + 4b² – 4ab – 4c2

ii)       x⁴ + x² + 1

iii)      ( x + y )² – ( x – y )²

iv)     p² – 4pq + 4q² – 6p + 12

v)      √2x² + 3x + √2

vi)     6√3x2 – 47x + 5√3

vii)   x² – 51x + 378

viii)  8( x + y )³ – 27( x – y )³

ix)     32x⁴ – 500x

x)      x³ + 3x²y + 3xy² + y³ – 0.027

xi)     x⁶ - 729

xii)   a³ – b³ + 1 + 3ab

xiii)  2√2x³ + 16√2y³ + z³ – 12xyz

xiv)  ( 2x – 3y )³ + ( 4z – 2x )³ + ( 3y – 4z )³

xv)    ( 5x – 7y )³ + ( 9z – 5x )³ + ( 7y – 9z )³

PS : Revise the formulae before you attempt these questions