Express the polynomial as a product of linear factors.
ƒ(x)=3x^3+12x^2+3x-18
a. (x+3)(x+6)(x-1)
b. 3(x-1)(x+3)(x+2)
c. (x-2)(x+3)(x-3)
d. (x-3)(x+3)(x-2)

Option B -                  

Step-by-step explanation:

Given : Polynomial

To find : Express the polynomial as a product of linear factors?

Solution :

Factor of the polynomial

Taking 3 common

Now, We factor the cubic term by rational root theorem.

If a polynomial function has integer coefficients, then every rational zero will have the form   where  p  is a factor of the constant and  q  is a factor of the leading coefficient.

The possible roots of the polynomial function is

Now, we substitute the values in the polynomial if it is equal to zero then it is the root.

Substitute x=1

So, x=1 is one of the root.

Similarly we substitute all the values one by one.

The values satisfied is x=-2 and x=-3

Substitute x=-2

So, x=-2 is one of the root.

Substitute x=-3

So, x=-3 is one of the root.

So, The factors of is (x-1)(x+2)(x+3).

Therefore, The linear factor of the given polynomial is

So, Option B is correct.

b

step-by-step explanation:

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