Finding Values of a Polynomial . show f(x) in factorised form..is this correct

Find the values of a and b for the polynomial f(x) = 2x^3 + ax^2 - 4x+b. given that f(x) is divisible by
x+1 and x-3. Write f(x) in a factorized form. hint: (consider f(-1) and f(3)).

to find the values of and b..this is what i did:
f(-1) = 2(-1)^3 - a(-1)^2 - 4(-1) + b
-2 - 1a - 4 + b = 0
-1a + b = 6

f(3) = 2(3)^3 - a(3)^2 - 4(3) + b
54 - 9a -12 +b = 0
9a + b = -42
this gave me (-1a+b=6)/(9a+b=-42)
by using the substitution method i get:
9(6+b)/(-1)+b = -42
-54+10b=-42
-54+42 = -10b
-12 = 10b
b=-12/-10, b=1.2

sub 1.2 into a to get a=(6-1.2)/(-1) = 4.8/-1 = -4.8

so a = -4.8 and b = 1.2 ...is this correct?

and how do i show f(x) in factorized form?

right idea, but a math mistake...

f(-1) = -2 + a + 4 + b = 2 + a + b = 0 ==> a + b = -2
f(3) = 2(27) + 9a - 12 + b = 0 ==> 42 + 9a + b = 0 ==> 9a + b = -42

now you have:
a + b = -2
9a + b = -42
------------------ (subtract)
-8a = 40
a = -5
and if a = -5, then b = 3

so the function is f(x) = 2x^3 - 5x^2 - 4x + 3

since f(-1) = f(3) = 0, then (x + 1) and (x - 3) are factors

2x - 1 must be the other factor to get the leading term and constant right
you can multiply it back out to confirm

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

(x^2 - 2x - 3)(2x - 1) = 2x^3 - 5x^2 - 4x + 3 works... (and x = 1/2 is the other zero ==> f(1/2) = 0)

f(-1) = -2+a+4+b = 0
f(3) = 54+9a-12+b = 0
a+b+2 = 0
9a+b+42 = 0
8a + 40 = 0
a = -5
b = 3
f(x) = 2x^3 - 5x^2 -4x + 3
f(x) = (x+1)(x-3)(2x-1)

Your calculations are wrong:

x+1 = 0 --> x=-1

f(-1) = 2(-1)^3 +a(-1)^2 -4(-1) + b = -2 + a + 4 +b = 0 ---> a+b = -2

x-3 = 0 ----> x = 3 and f(3) = 0 so

f(3) = 2(3)^3 +a(3)^2 -4(3) + b = 54 + 9a -12 +b = 0 ---> 9a +b = -42


(9a + b) - (a + b) = 9a + b -a - b= 8a = -42 - (-2) = -40