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Question

If (x3) and (x2) are two factors of the polynomial x36x2+11x6,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 x1
Since (x-3) and (x-2) are the factors of the given polynomial, the product of (x-3) and (x-2) (x3)(x2)=x22x3x+6=x25x+6will also be a factor of the polynomial.

Now, for finding the third factor,divide the polynomialx36x2+11x6 by (x25x+6).

x25x+6x1)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x36x2+11x6 x35x2± 6x +0–––––––––––––––––––– x2 + 5x 6x2 ± 5x 6––––––––––––––– 0

(x1) is the third factor.

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