MATH101 Tutorial 6 ADGJKK DGJK DFGHJK DFGHJK XCVBN FGHJMK, DFGHJ DFGHM FGHJK HNJ PDF

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MATH 101 Tutorial 6 Department of Mathematics, Botswana International University of Science and Technology 29 January – 2 February 2018 —————————————————————— Question 1 : Find the product of the following polynomial expressions (a) (2x + 3)(x − 4)

(x + 1)(x2 + 3x − 5)

(b)

(c)

(2x2 − 3)(x3 + 5)

Question 2 : Factorize the following polynomials into linear and/or irreducible quadratic terms (a) 3x2 + 8x + 4

(b)

64 − x6

(c) 3x4 − 3x3 − 36x2

(d)

x5 − 4x3 − x2 + 4

Question 3 : Use long division to find the quotient and remainder form as in P (x) = Q(x)D(x) + R(x); (a) P (x) = x3 + 2

if

and D(x) = x2 + 3x + 2

(b) P (x) = 2x4 + x2 + x − 5

and D(x) = 3x2 + 1

Question 4 : Determine the remainder when P (x) is divided by x − c for: (a) P (x) = x4 − 7x2 + 4x + 20;

c = 1 and c = −2.

(b) P (x) = 2x3 − 7x2 + 4x + 3;

3 c = −1 and c = . 2

Question 5 : Find rational zeros of the following polynomials and use this information to factor completely the polynomials. (a)

2x3 − 10x2 − 9x + 3

x4 − 6x3 + 14x2 − 14x + 5.

(b)

Question 6 : Simplify the following rational functions to write them in simplest form (a) f (x) =

x2 − 9 6x + 18

(c) h(x) =

x3 + 2x2 − 3x − 6 x3 + 8

(b)

g(y) =

2y 2

2y + 1 − 11y − 6

Question 7 : Find the partial fraction decomposition of: (a) f (x) =

5x + 7 2 x + 2x − 3

(b) g(x) =

6x2 − 14x − 27 (x + 2)(x − 3)2

(c) (d)

g(x) =

5x2 − 8x + 5 (x − 2)(x2 − x + 1)

r(x) =

x3 + 2 (x + 1)(x + 2)...