Question

When factored completely, which is a factor of 6x3 - 12x2 - 48x

Answer 1

Assignment:
`\bold{Simplify \ 6\cdot \:3-12\cdot \:2-48x}`

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Answer:
`\bold{-48x-6}`

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Explanation:
`\downarrow\downarrow\downarrow`

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[ Step One ] Multiply Numbers:
`\bold{6\cdot \:3=18}`

`\bold{18-12\cdot \:2-48x}`

[ Step Two ] Multiply Numbers:
`\bold{12\cdot \:2=24}`

`\bold{18-24-48x}`

[ Step Three ] Subtract Numbers:
`\bold{18-24=-6}`

`\bold{-48x-6}`

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`\bold{\rightarrow Rhythm \ Bot \leftarrow}`

Answer 2

Two factors of 6x^3 - 12x^2 - 48x are 6x and x.

Step-by-step explanation:

Identify common factors: Look for the greatest common factor (GCD) of all terms. In this case, it's 6x.

Factor out the GCD: Divide each term by 6x:

6x^3 / 6x = x^2

12x^2 / 6x = 2x

48x / 6x = 8

Rewrite the expression with the factored GCD:

6x^3 - 12x^2 - 48x = (6x) * (x^2 - 2x - 8)

Further factorization: The remaining polynomial, x^2 - 2x - 8, can be factored further by grouping or using the quadratic formula. It has roots of -4 and 2, so its factored form is:

x^2 - 2x - 8 = (x + 4)(x - 2)

Combined factors: Putting together the GCD and the factored remaining term, the complete factorization of 6x^3 - 12x^2 - 48x is:

6x(x + 4)(x - 2)

Therefore, 6x and x are factors of 6x^3 - 12x^2 - 48x. The complete factorization includes additional terms found by further factoring the remaining polynomial.