Question

When factored completely, which is a factor of 3x3 − 9x2 − 12x A. L(x − 3) B. (x − 4) C. (3x − 1) D. <(3x − 4)

Answer 1

`3x^3-9x^2-12x`

Step 1:

Factor out the common term

The common term is 3x

By doing this, we will have

`\begin{gathered} 3x^3-9x^2-12x=3x((3x^3)/(3x)-(9x^2)/(3x)-(12x)/(3x)) \\ =3x(x^2-3x-4) \end{gathered}`

Step 2:

Factorise the quadratic expression in the bracket

`3x(x^2-3x-4)`

By doing this, we will have to look for two factors to multiply to give i4 and if we add them together, we will have -3

The two factors are -4 and +1

therefore,

Replace -3x with -4x + x

`\begin{gathered} 3x(x^2-3x-4) \\ =3x(x^2-4x_{}+x-4) \\ =3x(x(x-4)+1(x-4) \\ =3x(x+1)(x-4) \end{gathered}`

Hence,

The final answer is = (x-4)