1
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Question

# If (xâˆ’3) and (xâˆ’2) are two factors of the polynomial x3âˆ’6x2+11xâˆ’6,then find the third factor.

A
x1
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B
x5
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C
x4
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D
x6
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Solution

## The correct option is A x−1Since (x-3) and (x-2) are the factors of the given polynomial, the product of (x-3) and (x-2) (x−3)(x−2)=x2−2x−3x+6=x2−5x+6will also be a factor of the polynomial. Now, for finding the third factor,divide the polynomialx3−6x2+11x−6 by (x2−5x+6). x2−5x+6x−1)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x3−6x2+11x−6 −x3∓5x2± 6x +0–––––––––––––––––––––– −x2 + 5x− 6∓x2 ± 5x ∓6––––––––––––––––– 0 ∴(x−1) is the third factor.

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