What is the factor form for x^3-x^2-6x?

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To start off, everything that has a factor of x in common so . . factor out the x -- this means divide each term by the x.

x(x^2 - x - 6)

Now you will go through the some what laborious process of factor the remaining trinomial . ....

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To start off, everything that has a factor of x in common so . . factor out the x -- this means divide each term by the x.

x(x^2 - x - 6)

Now you will go through the some what laborious process of factor the remaining trinomial . . .

make a list of factors of 6 (I'll ignore the sign for now)

1 * 6

2 * 3

No using these factors and assigning signs as you might need them to make it work . . .can you add or subract to find -1, the coeffiecient of the middle term?

1+6 = 7, -1 + -6 = -7, -1 + 6 = 5 . . .this combo just won't work

2 + -3 = -1 . . .so use 2 and -3 when we go back to rewrite the problem . . .

x(x^2 + 2x + -3x - 6) next group and factor the smaller groups

x[ (x^2 + 2x) + (-3x - 6)]

looking at (x^2 + 2x) they have a x in common so

x(x + 2)

looking at (-3x - 6), they have a -3 in common so . .

-3(x + 2) -> remember -6/-3 = +2

so now we have . . .

x[x(x + 2) + -3(x + 2)]

Notice that there is a matching (x + 2) for each grouping . . if you pull this out front .. . you will use the rest as the final factor . . . .

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

This is your factored form!

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