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Factorising cubic

  • #1

Homework Statement


The curve C with equation y = f(x) passes through the point (5, 65).
Given that f'(x) = 6x2 -10x - 12,
a) use integration to find f(x)
b) Hence show that f(x) = x(2x+3)(x-4)

The Attempt at a Solution


I have no problem with this question, except it seems the given function for b) might be wrong or at least not complete.
a) integrated for y = 2x3 - 5x2 - 12x + c
65 = 2(5)3 - 5(5)2 - 12(5) + c
= 200 - 125 - 60 + c = 15 + c.
65 - 15 = 50 = c,
Therefore y = 2x3 - 5x2 - 12x + 50.
b) Taking out x, we get x(2x2 - 5x - 12) + 50.
This factors into x(2x+3)(x-4) + 50. So the given function is missing the +50. My fault or printing error?
 

Answers and Replies

  • #2
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10,479
2*53 is not 200.
 
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  • #3
2*53 is not 200.
Argh... thanks. I went over that 4 or 5 times and didn't catch it out.
 
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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Homework Statement


The curve C with equation y = f(x) passes through the point (5, 65).
Given that f'(x) = 6x2 -10x - 12,
a) use integration to find f(x)
b) Hence show that f(x) = x(2x+3)(x-4)

The Attempt at a Solution


I have no problem with this question, except it seems the given function for b) might be wrong or at least not complete.
a) integrated for y = 2x3 - 5x2 - 12x + c
65 = 2(5)3 - 5(5)2 - 12(5) + c
= 200 - 125 - 60 + c = 15 + c.
65 - 15 = 50 = c,
Therefore y = 2x3 - 5x2 - 12x + 50.
b) Taking out x, we get x(2x2 - 5x - 12) + 50.
This factors into x(2x+3)(x-4) + 50. So the given function is missing the +50. My fault or printing error?
For future reference, a solitary factor of x implies that the constant term is zero in the full polynomial.
 

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