Department of Mathematics and Computer Science
NATIONAL UNIVERSITY OF LESOTHO
M1511
Tutorial 04
September 2025
[1] Perform the indicated operations and simplify:
x + 2 x
(a) (5y 2 − 7y + 3) − (2y 2 − 8y + 1)
(d)
+1
2
2
(b) (3x2 − 2y 2 )3
x4 − 1
(e) 2
x +1
2
√
√
1
1
1
(c) t +
(f)
x− y
x+ y
t
[2] Factorise the following expressions fully:
(a) 16x2 − 24x + 9
(e) (p − 2p)2 − 2(p − 2p) − 3
(b) (x − 7)2 − 49
(f) x5 + x4 + x + 1
(c) (2a + 3b)2 − (2a − 3b)2
(g) x 2 − x 2
(d) x6 − 8y 3
(h) (x2 + 3)− 3 − 23 x2 (x2 + 3)− 3
3
1
1
4
[3] Classify each of the following as monomial,binomial, trinomial, polynomial or neither.
State the degree where appropriate.
√
(a) 0
(c) 3 17x3 − 5
(e) 5x4 − 4x−1
√
(b) −57
(d) f (x) = 2 + 3x − 1
(f) a3 + b3 + c3 + 4abc
[4] Perform the following operations and write the answer in simplest form
2
2
3x + 2
y −y−6
y + 3y − 4
(a)
−2
(d)
x+4
y 2 + y − 12
y 2 + 2y − 3
1
2
3
2
2
(b)
−
+
(e) 2 −
÷ 2−
x + 1 (x + 1)2 x2 − 1
x
x
2
2
3
7
(f)
− 3 ÷h
(c)
+
3
(x + h)
x
5t 3t
[5] Find the domain of the following expressions.
1−x
x
(d)
(b)
x−3
x2 − 9
(e)
(c)
5
x3 + 1
(a)
√
3
x+3
x6 − 6x3 + 12x2 − 8
√
x+ 2
9y 3 + 9y 2 − y 2 + 2
(f)
2
y+
3
1