Find all rational roots of fx 6x5 11x4 9x3 9x3 13x2 3x

Find all rational roots of f(x) = 6x^5 + 11x^4 - 9x^3 - 9x^3 - 13x^2 + 3x + 2, a nd write f(x) in factorized form.

f(x)= 6x^5 + 11x^4-9x^3-13x^2 + 3x+2

Factors of constant are +-1,2

Factors of leading coefficient +-1,2,3,6

Possible roots +-1/1,+-2/1,+-1/2,+-2/2,+-1/3,+-2/3,+-1/6,+-2/6

We have to check each roots using synthetic division and the roots that gives the remainder zero are the required roots

And on using synthetic division,we find that 1,-1,-2,1/2,-1/3 will give us a remainder zero

Therefore the required rational zeroes are x=1,x=-1,x=-2,x=1/2,x=-1/3

and to find the factor form,we first move the terms from the right side and set it to zero

x-1=0,x+1=0,x+2=0,2x-1=0,3x+1=0

And multiply all the left terms together and that will be the factor form

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