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# Core 4 OCR past paper question 9

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1. Hi.
For question 9 (ii) i used trial and error with the factor theorem to find a factor that i could divide the equation by, is there a better method?
https://983c9f06eb1f75af6e83364e092b...20C4%20OCR.pdf
Thanks
2. (Original post by SamuelN98)
Hi.
For question 9 (ii) i used trial and error with the factor theorem to find a factor that i could divide the equation by, is there a better method?
https://983c9f06eb1f75af6e83364e092b...20C4%20OCR.pdf
Thanks
There's no better method.
3. (Original post by notnek)
There's no better method.
To solve this cubic we search for an integer solution and find p=5. If you have a graphical calculator, this is particularly easy and possibly even easier than trial and error. I believe that you are allowed these calculators in Core 4
4. (Original post by nerak99)
To solve this cubic we search for an integer solution and find p=5. If you have a graphical calculator, this is particularly easy and possibly even easier than trial and error. I believe that you are allowed these calculators in Core 4
p = -1 will be generally easier to find.
5. Rational root theorem to cut down on the number of trial and error solutions?
6. (Original post by nerak99)
To solve this cubic we search for an integer solution and find p=5. If you have a graphical calculator, this is particularly easy and possibly even easier than trial and error. I believe that you are allowed these calculators in Core 4
How do you do this on a calculator?
7. If you have a graphical calculator the you can plot the function and see that you will have roots at -1, +5, -4. Hence you know that the thing factorises to (x+4)(x+1)(x-5).

As for easier to spot a negative root by trial and error, it depends on how many 'tables' you know and shouted 5 to me.

But then I am pretty old.
8. A cheaper calculator (the Casio fx83... I think, but the common current Casio anyway) will do a table of values for you.

You can plug in the function and start from (say) -5, step in 1s up to +5 or so and view the table. You will see the zeroes at -4, -1 and +5

The fx83GT does have a tendency to run out of memory with complex functions but a cubic should be OK for that range
9. (Original post by nerak99)
As for easier to spot a negative root by trial and error, it depends on how many 'tables' you know and shouted 5 to me.
It screamed -1 for me
10. (Original post by nerak99)
As for easier to spot a negative root by trial and error, it depends on how many 'tables' you know and shouted 5 to me.
I'll have to agree with notnek here, the 1, -21 and -20 just shouted for a -1.
11. Well I guess you just has to be there.

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