2. The polynomial 3x3 – 2x2 – 12x + 8 is denoted by f(x). (a) Use factor theorem to show that (x + 2) is a factor of f(x).

see below

Step-by-step explanation:

to understand thisyou need to know about:factor theoremPEMDASgiven:f(x)=3x³-2x²-12x+8-a×-b=ab-a×b=-aba²-b²=(a+b)(a-b)to do:use factor theorem to show that (x+2) is a factor of f(x)tips and formulas:When f(c)=0 then x−c is a factor of f(x)let's solve:

according to the question

x+2=0

x=-2

therefore

we have proven that x+2 is a factor of 3x³-2x²-12x+8

let's factorise 3x³-2x²-12x+8

factor out x²: x²(3x-2)-12x+8factor out -4: x²(3x-2)-4(3x-2)group: (x²-4)(3x-2)use a²-b² = (a+b)(a-b): (x+2)(x-2)(3x-2)

and

we are done

Logical equivalent of the give question is its contrapositive

What are the options