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Answer:
<h2>see below</h2>Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>- factor theorem
- PEMDAS
- f(x)=3x³-2x²-12x+8
- -a×-b=ab
- -a×b=-ab
- a²-b²=(a+b)(a-b)
- use factor theorem to show that (x+2) is a factor of f(x)
- When f(c)=0 then x−c is a factor of f(x)
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+8
- factor 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