Question

Factoriz x³+6x²+11x+6 using factor theoram​

Answer 1

Zeroes of x

3

−6x

2

+11x−6

By using rational theorem, the roots can be among the factors of

1

6

=6

Let us try x=1

⇒(1)

3

−6(1)

2

+11(1)−6=0

∴(x−1) is a factor of x

3

−6x

2

+11x−6.

Now, using synthetic division method :

So, the quotient =x

2

−5x+6

Now, using common factor theorem,

⇒x

2

−5x+6=x

2

−2x−3x+6

=x(x−2)−3(x−2)

=(x−2)(x−3)

∴ Zeroes of the polynomial =1,2,3

So, factor of the polynomial =(x−1)(x−2)(x−3).

Hence, the answer is (x−1)(x−2)(x−3)

Answer 2

Answer:

hence the ans is {x-1) (x-2) (x-3)