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

Sagot :

Solution:

[tex]3x^3-9x^2-12x[/tex]

Step 1:

Factor out the common term

The common term is 3x

By doing this, we will have

[tex]\begin{gathered} 3x^3-9x^2-12x=3x(\frac{3x^3}{3x}-\frac{9x^2}{3x}-\frac{12x}{3x}) \\ =3x(x^2-3x-4) \end{gathered}[/tex]

Step 2:

Factorise the quadratic expression in the bracket

[tex]3x(x^2-3x-4)[/tex]

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

[tex]\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}[/tex]

Hence,

The final answer is = (x-4)

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