C1 Polynomial Roots

So I literally spent an hour trying to do this question with no luck. Long division doesn't work with it and I've tried completed the square. Any help would be appreciated. I know how to do (ii) and (iii) but I can't seem to work out (i).

Original post by JackB784

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Divide the cubic by x - 2. Post your attempt if you think it is wrong.

Reply 2

TenOfThem

18

Are you saying that you cannot do the long division for

(x^3 + 0x^2 - 5x + 2)\div(x-2)

You could always use inspection/equating coefficients

x^3 - 5x + 2 = (x-2)(x^2 + ax - 1)

(edited 9 years ago)

Reply 3

JackB784

OP

7

Original post by Mr M

Divide the cubic by x - 2. Post your attempt if you think it is wrong.

Yeah 1 sec I'll upload it.

Reply 4

atsruser

11

Original post by JackB784

So I literally spent an hour trying to do this question with no luck. Long division doesn't work with it and I've tried completed the square.

Long division works fine, so you've probably made a mistake. Complete the square on the remaining quadratic, then use difference-of-two-squares to factorise.

Reply 5

JackB784

OP

7

Original post by Mr M

Divide the cubic by x - 2. Post your attempt if you think it is wrong.

Reply 6

atsruser

11

Original post by JackB784

From that picture it's clear that you need to revise polynomial long division. You haven't completed the division, but more importantly, you haven't aligned the expressions correctly. You need to leave space for the missing

x^2

term in the cubic, for example. If you don't do that, you'll find it very tough to get the right answer.

Reply 7

JackB784

OP

7

Original post by atsruser

From that picture it's clear that you need to revise polynomial long division. You haven't completed the division, but more importantly, you haven't aligned the expressions correctly. You need to leave space for the missing

x^2

term in the cubic, for example. If you don't do that, you'll find it very tough to get the right answer.

Ah yes! Thank you I'll try again.

Reply 8

Tytrox

Original post by JackB784

So I literally spent an hour trying to do this question with no luck. Long division doesn't work with it and I've tried completed the square. Any help would be appreciated. I know how to do (ii) and (iii) but I can't seem to work out (i).