Fundamental of Mathematics
Tutorial 2
1.
2.
Determine which of the following are polynomial functions. If the function is a
polynomial, state its degree.
a.
f x   2 x 4  x
b.
g x   2
c.
h x   2 x  1
d.
Fx  
3
 x2
x
Identify the term for the following polynomial
6 x9  8 x 6 y 4  x 7 y  3xy 5  4
Solution:
a. Term
b. Degree
c. Coefficient
d. Degree of this polynomial
e. Leading term
f. Constant term
3.
Solve the following questions
a.
(x2 + 3x + 1) + (4x2 +5)
b.
4.
(2a2+3ab+4b2) + (7a2+ab-2b2)
Evaluate each polynomial function
a. f x   3x 2  10
b. gy   6 y 2  11y  20
Find f(-1) and g(3).
T2 - 1
Prepared by Wu Z.H.
5.
Multiply
a.
(y + 4)(y – 3)
b.
(2a – 3b)(2a + 4b)
c.
(2x - 5)(x2 - 5x + 4)
d.
(2p + 1)(p2 – 3p + 4)
6.
Find the quotient and the remainder for
a.
2x 3  9x 2  15
2x  5
b.
x 4  5x 3  10x 2  9x  34
x2
7.
Solve the following quadratic equations (where possible).
2 x 2 - 19 x - 10 = 0
a.
x2 + x + 1 = 0
b.
8.
Simplify the inequalities and graph the solution set.
a.
b. 21x  19  4 x  15
2 x < 3x + 7
T2 - 2
Prepared by Wu Z.H.