Let Px 2x3 5x2 4x 3 a List all possible rational zeros of

Let P(x) = 2x^3 5x^2 4x + 3.

(a) List all possible rational zeros of P. (Enter your answers as a comma-separated list.)

(b) Find the complete factorization of P.

P(x)= 2x³-5x²-4x + 3

a. To find the possible rational zeroes,we have to use rational zero test

Here constant is 3 and leading coefficient is 2

Factors of constant = +-1,3

Factors of leading coefficient=+-1,2

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

b. on using synthetic division for x-3 we get 2x^2 +x-1

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

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

c. To find the zeroes,we have to plug f(x)=0

(x-3)(x+1)(2x-1)=0

x=3,-1,1/2