Eric Nicholas K's answer to Dylan Lim's Secondary 4 A Maths Singapore question.
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Good evening Annie! Here are my workings for this question.
This is an unusual question.
The fact that f(x) has a factor x (equivalently, a factor “x - 0”) means that when f(x) is divided by “x - 0”, the remainder is f(0) = 0 times other terms which remains zero.
Let me know if you need more explanation on this.
This is an unusual question.
The fact that f(x) has a factor x (equivalently, a factor “x - 0”) means that when f(x) is divided by “x - 0”, the remainder is f(0) = 0 times other terms which remains zero.
Let me know if you need more explanation on this.
Date Posted:
4 years ago
Note that the second equation f(x) - f(x - 1) = 3x2 + 5x - 8 holds true for any value of x, so we can choose x = 0 so that
f(0) - f(-1) = -8
where f(0) = 0 as I explained earlier.
So, 0 - f(-1) = -8, leaving f(-1) = 8.
This statement suggests that the remainder when f(x) is divided by x + 1 is -8.
f(0) - f(-1) = -8
where f(0) = 0 as I explained earlier.
So, 0 - f(-1) = -8, leaving f(-1) = 8.
This statement suggests that the remainder when f(x) is divided by x + 1 is -8.
What does f(x-1) mean? Does it mean substituting all the x in f(x) with "x-1"?
Yup!
Let’s say
f(y) = 3y2 - cos y + 1/y
Then f(x + 5)
= 3 * (x + 5)^2 - cos (x + 5) + 1/(x + 5)
Let’s say
f(y) = 3y2 - cos y + 1/y
Then f(x + 5)
= 3 * (x + 5)^2 - cos (x + 5) + 1/(x + 5)
But in this situation it’s difficult to find the actual function f(x) because we are only given that the difference between f(x) and f(x - 1) is 3x2 + 5x - 8. The original f(x) contains a factor x.
The remainder should be 8 instead of -8 in the working.
Anyway Annie you can take a look at an alternative approach I wrote in the main comments. Longer but might be useful in other questions
Anyway Annie you can take a look at an alternative approach I wrote in the main comments. Longer but might be useful in other questions
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