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secondary 4 | A Maths
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Arennea Golen
Arennea Golen

secondary 4 chevron_right A Maths chevron_right Singapore

Help me!! I have math EOYs tomorrow

Date Posted: 4 years ago
Views: 318
J
J
4 years ago
The difference between the degree of the remainder and the degree of the divisor is at least 1.

This means it can be smaller than the divisor by 1 or more.


Since the divisor (x - 1)(x - 2) = x² - 3x + 2, the degree of the divisor is 2. So the degree of the remainder can be at most 1 or at lowest 0.

So we can let the remainder be in the form ax + b
J
J
4 years ago
So the polynomial f(x) can be expressed as


f(x) = (x - 1)(x - 2)(quotient) + ax + b

Since the remainder is 2 when divided by (x - 1),

f(1) = 2

(2 - 1)(2 - 2)(quotient) + a(1) + b = 2
a + b = 2
b = 2 - a


Since the remainder is 3 when divided by (x - 2),

f(2) = 3

(1 - 1)(1 - 2)(quotient) + a(2) + b = 3
2a + b = 3

Sub b = 2 - a,

2a + 2 - a = 3
a = 1

So b = 2 - 1 = 1


The remainder is x + 1.

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Arnold K H Tan
Arnold K H Tan's answer
2088 answers (A Helpful Person)
1st
AT
Arennea Golen
Arennea Golen
4 years ago
Thanks so much!
Arnold K H Tan
Arnold K H Tan
4 years ago
Most welcome. All the best for your paper!
J
J
4 years ago
I actually posted my version of the answer some 7 hours ago in the main comments section, but I guess you've probably missed it.

Anyway , do take note that the degree of the remainder is at most 1 smaller than the degree of the divisor. It may be 1 smaller or more degrees smaller.

So if you get A = 0 for similar questions when your divisor has a degree of 2, don't worry as it can just mean your remainder is a constant
Arennea Golen
Arennea Golen
4 years ago
Thanks too, J :)
Arennea Golen
Arennea Golen
3 years ago
Thanksss
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syjiaxuan
Syjiaxuan's answer
290 answers (A Helpful Person)
Hope this helps, parts in pink are impt
Arennea Golen
Arennea Golen
4 years ago
Thank you!