- x^6 y^6 x^3 y^3 6 18. a^8 a^4 2
- a^2 b^2 8 ab 105 20. x^2 37 a 650
- 4 x^4 25 x^2 36 22. 12 x^2 38 x 20
- 9 x^2 y^2 5 xy^2 14 y^2 24. 4 x^4 27 x^2 81
- ax^2 (a^2 1 )xa 26. 3 (a^2 2 a)^2 22 (a^2 2 a) 40
- 14 (xz)^2 29 (xz)(x 1 ) 15 (x 1 )^2
- ( 4 a 3 b)^2 2 ( 4 a 3 b)(a 2 b) 35 (a 2 b)^2
- (a 1 )x^2 a^2 xy(a 1 )y^2 30. 24 x^4 3 x
- (a^2 b^2 )^3 8 a^3 b^3 32. x^3 3 x^2 3 x 2
- a^3 6 a^2 12 a 9 34. a^3 9 b^3 (ab)^3
- 8 x^3 12 x^2 6 x 63 36.
27
83
a^3 b- 8
3 1
a 38.^66
27b
a
- a
a
aa
1
2 4
41
42 2 40. ( 3 a 1 )^3 ( 2 a 3 )^3- (x 5 )(x 9 ) 15 42. (x 2 )(x 3 )(x 4 )(x 5 ) 48
- (x 1 )(x 3 )(x 5 )(x 7 ) 64
- Show that, x^3 9 x^2 26 x 24 (x 2 )(x 3 )(x 4 )
- Show that, (x 1 )(x 2 )( 3 x 1 )( 3 x 4 ) ( 3 x^2 2 x 1 )( 3 x^2 2 x 8 )
3 ⋅5 Remainder Theorem
We observe the following example :
If 6 x^2 7 x 5 is divided by x 1 , the what is quotient and remainder?
Dividing 6 x^2 7 x 5 by x 1 in common way, we get,
x 1 ) 6 x^2 7 x 5 ( 6 x 1
6 x^2 6 x15
xx4Here,x 1 is divisor, 6 x^2 7 x 5 is dividend, 6 x 1 is quotient and 4 is remainder.
We know, dividend = divisor u quotient + remainder