Polynomials

1.
s = (2/5)(t + 2)
5s = 2t + 4
2t = 5s - 4
t = (5s - 4)/2

When s = s1:
t = (5s1 - 4)/2

When s = s1 - 2:
t = [5(s1 - 2) - 4]/2
t = [(5s1 - 4) - 10]/2
t = (5s1 - 4)/2 - 5

When s decreases by 2:
Decrease in t
= (5s1 - 4)/2 - [(5s1 - 4)/2 - 5]
= 5

2.
3(m - 1) = n - m - 3
3m - 3 = n - m - 3
4m = n
m = n/4

n = 4m
When m = 2, n = 4(2) = 8
When m = 4, n = 4(4) = 16

% increase in the value of n
= [(16 - 8)/8] x 100%
= 100%

3.
(a)
A = (3)•(5) - 2(x)•(y)
A = 15 - 2xy

(b)
2xy = 15 - A
y = (15 - A)/(2x)

4.
an + an-1 - 6an-2
= a2•an-2 + a•an-2 - 6•an-2
= an-2(a2 + a - 6)
= an-2(a + 3)(a - 2)

5.
4(x2 + y2) - 2(x2 - y2)
= 4x2 + 4y2 - 2x2 + 2y2
= 2x2 + 6y2
= 2(x2 + 3y2)
=

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