1. Check whether g(x) = 1 x is a factor of p(x) = 3x
2 x – 1.
2. Check whether g(x) = x 1 is a factor of p(x) = x
3 1.
3. Find the value of ‘k’, if x 1 is a factor of p(x) = kx
2 – x – 4.
4. Factorise 2x
2 3x 1.
5. Factorise x
3 – 2x
2 – 5x 6.
6. Use suitable identities to find the following products:
(i) 105 x 106 (ii) 104
3
7. Expand:
(i) 3a 4b 5c
2
(ii) 3a 4b
3
8. Factorise: 125x
3
- 27y
3 8 90xy.
9. Verify that : (i) x
3 y
3 = (x y)(x
2
- xy y
2
)
(ii) x
3
- y
3 = (x - y)(x
2 xy y
2
)
10.Verify that :
x
3 y
3 z
3
- 3xyz = 1
2
(x y z)[(x − y)
2 (y − z)
2 (z − x)
2
]