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Factor completely 3x3 + 3x2 − 18x.


3x(x + 3)(x + 2)

3x(x + 3)(x − 2)

3x(x − 3)(x + 2)

3x(x − 3)(x − 2)

Verified Answer :

brandoncarroll16

3x(x − 3)(x − 2)hope this helps

Answer:  The correct option is

(B) \(3x(x+3)(x-2).\)

Step-by-step explanation:  We are given to completely factor the following cubic expression :

\(E=3x^3+3x^2-18x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

Since the given expression does not contain the constant term, so we will take out the x-term and then factorize the remaining quadratic expression.

The factorization of the given expression (i) is as follows :

\(E\\\\=3x^3+3x^2-18x\\\\=3x(x^2+x-6)\\\\=3x(x^2+3x-2x-6)\\\\=3x(x(x+3)-2(x+3))\\\\=3x(x+3)(x-2).\)

Thus, the complete factored form of the given expression is \(3x(x+3)(x-2).\)

Option (B) is CORRECT.

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