2math questions for１０ｐｏｉｎｔｓ

1.
Monthly salary of the 1st year = $550
Monthly salary of the 2nd year = $(550 + 35)
Monthly salary of the 3rd year = $(550 + 35 × 2)
......
Monthly salary of the 10th year = $(550 + 35 × 9)

The monthly salaries form an A.S. (in $) with
First term, a = 550
Common difference, d = 35
No. of terms, n = 10

Total amount of salary
= $[2a + (n - 1)d] × (n / 2) × 12
= $[550 × 2 + 9 × 35] × (10 / 2) × 12
= $84900


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2.
972 = 16x³ + 156x²
16x³ + 156x² - 972 = 0
4x³ + 39x² - 243 = 0

Let f(x) = 4x³ + 39x² - 243

f(-3) = 4(-3)³ + 39(-3)² - 243 = 0
(x + 3) is a factor of f(x).

4x³ + 39x² - 243 = 0
(4x³ + 12x²) + (27x² + 81x) + (-81x - 243) = 0
4x²(x + 3) + 27x(x + 3) - 81(x+ 3) = 0
(x + 3)(4x² + 27x - 81) = 0
(x + 3)(x + 9)(4x - 9) = 0
x = -3 .or. x = -9 .or. x = 9/4

2015-03-08 13:16:19 補充：
2.
The question is on solving the equation, but NOT ONLY factorization.

1) 550 x 12 + (550+35) x 12 + (550+2 x 35) x 12 + ....... +(550+9 x 35)x12
= 12[550+(550+35)+(550+2 x 35) + .... (550+9 x 35)]
= 12[(10/2)(2 x 550 + 9x35]
= $84900

2) 16x^3 + 156x^2 - 972 = (4x-9)(x+3)(x+9)
考試通常會係A PART比TIPS你 叫你TEST咩係佢既FACTOR,如F(3)=0
X-3 IS A factor of f(x). 網上面亦有計算機program解三次方程,你可以入機

2015-03-08 00:14:58 補充：
你知道其中一個factor就再用長除法

但係咁計費時

最好用program

2015-03-08 00:16:06 補充：
題一,

其實係考緊 AS 和

公式: n/2 [2a+(n-1)d]