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Algebra

New kid on the Block

 Joined: 1 Feb 2011 Post: 2
1 Feb 2011 06:43:55 IST
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Factor x^3-10x^2+29x-20
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Factor x^3-10x^2+29x-20

New kid on the Block

Joined: 1 Feb 2011
Posts: 2
1 Feb 2011 06:53:05 IST
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Duh

New kid on the Block

Joined: 28 Jan 2011
Posts: 4
1 Feb 2011 14:03:50 IST
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(x - 1)( x- 4 )( x - 5 )

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Joined: 16 Jan 2010
Posts: 318
1 Feb 2011 14:56:29 IST
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By trial we can see 1 is a zero of the polynomial P(x) = x3 - 10x2 + 29x - 20

So, either divide it by (x - 1) or write in such a way so that x - 1 comes out to be common.

As, P(x) = x3 - x2 - 9x2 + 9x + 20x - 20 = x2 (x - 1) - 9x (x - 1) + 20 (x - 1) = (x - 1)(x2 - 9x + 20)

= (x - 1)(x2 - 5x - 4x + 20) = (x - 1)[x(x - 5) - 4(x - 5)] = (x - 1)(x - 5)(x - 4)

Or, P(x) = (x - 1)(x - 4)(x - 5)

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