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Factor theorem/Remainder theorem help.

Ok so the question is

f(x) = x³+2ax²-20x-25

Given that the remainder when f(x) is divided by (x-3) is 14

a.) Find the value of a.

So to find a I subbed f(3) into the function and worked out that a = 4.

b.) Find the remainder when f(x) is divided by (2x+1)

so f(-1/2) but what confuses me is the 2ax² part. Assuming I worked out a being 4 correctly so do I do 4(-1/2)² * 2 = 2

And so my final answer would be f(-1/2) = (-1/2)³+2-20(-1/2)-25
Which equals -103/8

The only problem is this answer seems rather strange so I was hoping someone could give me a hand. Any help is appreciated.
Reply 1
Avatar for Notnek
Notnek
21
Original post by I_Like_Maths
Ok so the question is

f(x) = x³+2ax²-20x-25

Given that the remainder when f(x) is divided by (x-3) is 14

a.) Find the value of a.

So to find a I subbed f(3) into the function and worked out that a = 4.

b.) Find the remainder when f(x) is divided by (2x+1)

so f(-1/2) but what confuses me is the 2ax² part. Assuming I worked out a being 4 correctly so do I do 4(-1/2)² * 2 = 2
And so my final answer would be f(-1/2) = (-1/2)³+2-20(-1/2)-25
Which equals -103/8

The only problem is this answer seems rather strange so I was hoping someone could give me a hand. Any help is appreciated.

The line shown in green above is correct but your answer is wrong. Your answer is close to the correct answer and the correct answer is "strange" (in your words) like -103/8.

You'll find that A Level answers won't always be nice integers. -103/8 is a reasonable looking answer although in this case, wrong.
(edited 9 years ago)
Original post by notnek
The line shown in green above is correct but your answer is wrong. Your answer is close to the correct answer and the correct answer is "strange" (in your words) like -103/8.

You'll find that A Level answers won't always be nice integers. -103/8 is a reasonable looking answer although in this case, wrong.


Ah ok thanks man, So is my final answer -105/8 ?

I get paranoid a lot after one of my teachers told me most answers will end up being quite nice. If not you've probably made a mistake.
Reply 3
Avatar for Notnek
Notnek
21
Original post by I_Like_Maths
Ah ok thanks man, So is my final answer -105/8 ?

I get paranoid a lot after one of my teachers told me most answers will end up being quite nice. If not you've probably made a mistake.

That may be true in a Year 8 textbook but not A Level.
Original post by notnek
That may be true in a Year 8 textbook but not A Level.



Ah ok seems sensible, Sorry to waste your time but is -105/8 the right answer not completely sure if I did it right?:smile:
Reply 5
Avatar for Notnek
Notnek
21
Original post by I_Like_Maths
Ah ok seems sensible, Sorry to waste your time but is -105/8 the right answer not completely sure if I did it right?:smile:

Yes that's right.
Original post by notnek
Yes that's right.



Thank you very much for the help mate:smile:

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