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Question

using the factor theorem factorise the following
x36x2+11x6

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Solution

Zeroes of x36x2+11x6
By using rational theorem, the roots can be among the factors of 61=6
Let us try x=1
(1)36(1)2+11(1)6=0
(x1) is a factor of x36x2+11x6.
Now, using synthetic division method :


So, the quotient =x25x+6
Now, using common factor theorem,
x25x+6=x22x3x+6
=x(x2)3(x2)
=(x2)(x3)
Zeroes of the polynomial =1,2,3
So, factor of the polynomial =(x1)(x2)(x3).
Hence, the answer is (x1)(x2)(x3).

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