Question

246
Mathematics VIII
If z varies directly as x and inversely as y. Find the percentage increase in z duero
9.
increase of 12% in x and a decrease of 20% in y.
10.
If x + 1 men will do the work in x+1 days, find the number of days that (x+2) mene
finish the same work.
width and area will vary accordingly. Use the following table of values to look at how
Given a rectangle with a fixed perimeter of 24 meters, if we increase the length by Im
11.
What do you observe? Write your observations in your note books
3
5
4
6
2
7.
8
Length(in cm) 1
Width(in cm)
11
Area (in cm) 11
10
20
1​

Answer 1

Answer:

(i) Apply factor theorem  

x+1=0

So x=−1

2x  

3

+x  

2

−2x−1

Replace x by −1, we get

2(−1)  

3

+(−1)  

2

−2(−1)−1=−2+1+2−1=0

Reminder is 0 so that x+1 is a factor of 2x  

3

+x  

2

−2x−1  

(ii) Apply factor theorem  

x+2=0  

So x=−2  

x  

3

+3x  

2

+3x+1

Replace x by −2, we get

(−2)  

3

+3(−2)  

2

+3(−2)+1=−8+12−6+1=1

Reminder is 1 so that x+2 is not a factor of x  

3

+3x  

2

+3x+1

(iii) Apply factor theorem  

x−3=0  

So x=3  

x  

3

−4x  

2

+x+6

Replace x by 3, we get

(3)  

3

−4(3)  

2

+(3)−1=27−36+3+6=0

Reminder is 0 so that x−3 is a factor of x  

3

−4x  

2

+x+6