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If one zero of the polynomial p(x) = x3 – 6x2 + 11x – 6 is 3, find the other two zeroes.

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Best answer

p(x) = x3 – 6x2 + 11x – 6 and its factor, x + 3 

Let us divide p(x) by (x – 3). 

Here, x3 – 6x2 + 11x – 6 = (x – 3) (x2 – 3x + 2) 

= (x – 3) [(x2 – (2 + 1) x + 2] 

= (x – 3) (x2 – 2x – x + 2) 

= (x – 3) [x (x – 2) – 1(x – 2)] 

= (x – 3) (x – 1) (x – 2) 

∴The other two zeroes are 1 and 2.

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