Factor the expression completely: \(2x^3 - 2x^2 - 12x\).

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2 x 3 − 2 x 2 − 12 x = 2 x ( x 2 − x − 6 ) = 2 x ( x 2 − x − 2 x + 2 x − 6 ) = = 2 x [( x 2 − 3 x + 2 x − 6 )] = 2 x [ x ( x − 3 ) + 2 ( x − 3 )] = = 2 x ( x − 3 ) ( x + 2 )

Answered by Lilith | 2024-06-10

Extract a 2x from the expression to make it 2x(x^2-x-6). Factor out x^2-x-6:------------------>must factors must multiply to -6 and add to -1 -3 and 2 fit the criteria therefore x^2-x-6 factors out to (x-3)(x+2).
But dont forget to put it all back together. The 2x is part of the expression so the full factored expression is:
2x(x-3)(x+2)

Answered by argpirate | 2024-06-10

To factor the expression 2 x 3 − 2 x 2 − 12 x completely, we first factor out the GCF, which is 2 x . Then we factor the quadratic expression x 2 − x − 6 into ( x − 3 ) ( x + 2 ) . The complete factored form is 2 x ( x − 3 ) ( x + 2 ) .
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Answered by Lilith | 2024-12-23