Question

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).

Answer 1

Answer:

see below

Step-by-step explanation:

to understand this

you need to know about:

• factor theorem
• PEMDAS

given:

• f(x)=3x³-2x²-12x+8
• -a×-b=ab
• -a×b=-ab
• a²-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

1. $\sf substitute \: the \: value \: of \: x \: : \\ \sf 3 {( - 2)}^{3} - 2( { - 2)}^{2} - 12( - 2) + 8$
2. $\sf simplify \: exponets : \\ 3( - 8) - 2(4) - 12( - 2) + 8$
3. $\sf \: multiply : \\ \tt - 24 - 8 + 24 + 8$
4. $\sf simplify : \\ \sf- 32 + 32 \\ \sf0$

therefore

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

let's factorise 3x³-2x²-12x+8

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

• (x+2)(x-2)(3x-2)

and

we are done