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factor 3x^3-6x^2-24x

the teacher said that there were three different answers that could be true

i got one of them: (3x-12)(x+2), but how do you get any other answers?

G

factor 3x^3-6x^2-24x

the teacher said that there were three different answers that could be true

i got one of them: (3x-12)(x+2), but how do you get any other answers?

- Joined
- Feb 8, 2006

- Messages
- 44

you have to factor out 3x first to find the binomial

there is only one awnser

there is only one awnser

3x^3 - 6x^2 - 24xbrendaursula said:

factor 3x^3-6x^2-24x

the teacher said that there were three different answers that could be true

i got one of them: (3x-12)(x+2), but how do you get any other answers?

= 3x(x^2 - 2x - 8)

= 3x(x - 4)(x + 2) : now fully factored

The instruction 'Factor" always means "FactorFactor: \(\displaystyle \:3x^3\,-\,6x^2\,-\.24x\)

the teacher said that there were three different answers that could be true. . . . no!

i got one of them: \(\displaystyle (3x\,-\,12)(x\,+\,2)\), . . . incorrect

\(\displaystyle \;\;\)but how do you get any other answers?

First, take out any common factors: \(\displaystyle \,3x(x^2\,-\,2x\,-\,8)\)

Then factor the trinomials: \(\displaystyle \,3x(x\,+\,2)(x\,-\,4)\)

\(\displaystyle \;\;\)(The order of the factors makes no difference.)

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I hope you teacher realizes that it was a silly thing to say to a math class.

By his/her mind-set, there are

\(\displaystyle \;\;\;24\;=\;1\,\times\,24,\;\;2\,\times\,12,\;\;3\,\time\,8,\;\;4\,\times\,6\)

But there is only

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Even if your teacher is correct ... and we

\(\displaystyle \;\;\)there are

\(\displaystyle 3x^3\,-\,6x^2\,-\,24x\;=\)

\(\displaystyle \;\;3x(x\,+\,2)(x\,-\,4)\)

\(\displaystyle \;\;3(x^2\,+\,2x)(x\,-\,4)\)

\(\displaystyle \;\;3(x\,+\,2)(x^2\,-\,4x)\)

\(\displaystyle \;\;x(3x\,+\,6)(x\,-\,4)\)

\(\displaystyle \;\;x(x\,+\,2)(3x\,-\,12)\)

\(\displaystyle \;\;(3x^2\,+6x)(x\,-\,4)\)

\(\displaystyle \;\;(x\,+\,2)(3x^2\,-\,12x)\)

\(\displaystyle \;\;\)and, of course: \(\displaystyle \,1\,\times\,(3x^3\,-\,6x^2\,-\,24x)\)

It should be obvious why we should factor