factor X^3+X^2-6Xno

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

factor X^3+X^2-6X

first factor X

==> x(x^2+x-6)

Now factor the equation (x^2+x-6)

==> x(x+3)(x-2)

If you need to obtain the eqution's roots, then you need to find x values in which the equation equals 0

==> x(x+3)(x+2)=0

==> x = 0, -3, and -2


neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To factor x^3+x^2-6x


x^3+x^2-6x = x*x^2+x*x-x*6

Each term is a factor of x. So we can factor out x and rewite the given expression as:


The second factor x^2+x-6 in (1) by grouping the middle term   could be rewritten like:  x^2+3x-2x-6=


=(x+3)(x-2). Substituting this for x^2+x-6 in (1), we get:

x(x+3)(x-2) which is the factored form of  x^3+x^2-6

luvale's profile pic

luvale | Student, Grade 10 | (Level 1) eNoter

Posted on

So first take out the x so the equation looks like ax2+bx-c

Then you need to look at pairs of numbers that go into 6

2 x 3

6 x 1

Then you set up the equation as

x(x +/- _) (x+/- _)

so you see that before the second x the number is 1, meaning that when you add the two "_"'s together you need one. From this you can cross off 6 x 1 off your pairs and write

x(x+3) (x-2)

You can check this by adding the numbers together and getting positive one (the number needed) and multiplying and getting negative 6 (also the number needed)

Good luck!


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