polynomial division

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sidon: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Apr 09, 2010 11:29 am

by sidon » Tue Apr 27, 2010 12:46 pm

Hi I need help with the following :

find the value of k for whick the polynomial 2x^3-x^2+2x-k is idvisable by (x-1).

a.1
b.2
c.3
d.4
e.5

Thanks,
Sidon

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Source: Beat The GMAT — Quantitative Reasoning | Tue Apr 27, 2010 12:46 pm

iamseer: Master | Next Rank: 500 Posts; Posts: 170; Joined: Wed Jun 10, 2009 5:59 am; Thanked: 13 times

by iamseer » Tue Apr 27, 2010 1:46 pm

IMO answer 3

just simply divide the polynomial with (x-1)

"Choose to chance the rapids and dance the tides"

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sidon: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Apr 09, 2010 11:29 am

by sidon » Wed Apr 28, 2010 11:40 am

Can you please elaborate more on how ?

Thanks.

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4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

by 4GMAT_Mumbai » Wed Apr 28, 2010 11:52 am

Hi Sidon,

This is an application of the remainder theorem as described in https://en.wikipedia.org/wiki/Polynomial ... er_theorem

If the requirement is that the numerator is divisible by (x-1), the remainder is 0.

If the remainder is 0, it implies that f(1) should be equal to 0.

Just substituting x = 1 in the numerator equation and equating it to 0 yields the value of 'k' to be 3.

Hope this helps.

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