What is the completley factored form of f(x)=x^3-2x^2-5x+6

f(x) = (x - 1)(x + 2)(x - 3)

Step-by-step explanation:

We are given the following function and we are to factorize it completely:

To factorize this completely, we will use the rational roots theorem.

P = ± multiples of constant term

Q = ± multiples of the coefficient of highest degree term  

So the factors will be .

The possible rational roots are .

1 is a confirmed root and now we will use synthetic division to find the other rational roots:

1 | 1  -2  -5   6

        1   -1   -6

___________

   1   -1   -6   0    

So the polynomial will be which can we factorize now.

Therefore, the completely factorized form of the given function is f(x) = (x - 1)(x + 2)(x - 3).

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

5/12, or 5: 12

step-by-step explanation: