Simplify rational expressions

Krilian said:
How do I factor these?


11x^2 + 33x^3 <<<< What are the common functions in the first two terms - do we have anything common among the constant terms?

x^3 - x^2 - -2x + 2 <<<< Have you learned rational root theorem?
Click to expand...
 
Krilian said:
How do I factor these?


11x^2 + 33x^3

x^3 - x^2 - -2x + 2
Click to expand...

For your first problem, remember this: the VERY FIRST STEP in any factoring exercise is to remove the greatest common factor of all the terms.

You've got

11x[sup:2c8nk5jr]2[/sup:2c8nk5jr] + 33x[sup:2c8nk5jr]3[/sup:2c8nk5jr]

Or,

11x[sup:2c8nk5jr]2[/sup:2c8nk5jr]*1 + 11x[sup:2c8nk5jr]2[/sup:2c8nk5jr]*3x

Do you see that each term has a factor of 11x[sup:2c8nk5jr]2[/sup:2c8nk5jr]? Remove that common factor.

And for your second problem, before worrying about the Rational Root theorem, I'd try factoring by grouping. Group the first two terms together, and the last two terms together (and I THINK you may have omitted a grouping symbol):

x[sup:2c8nk5jr]3[/sup:2c8nk5jr] - x[sup:2c8nk5jr]2[/sup:2c8nk5jr] - (-2x + 2)

Distribute that " - " sign throught the parentheses:

x[sup:2c8nk5jr]3[/sup:2c8nk5jr] - x[sup:2c8nk5jr]2[/sup:2c8nk5jr] + 2x - 2

Now, group the first two terms together, and the last two terms together:

x[sup:2c8nk5jr]3[/sup:2c8nk5jr] - x[sup:2c8nk5jr]2=[/sup:2c8nk5jr] + 2x - 2

The first two terms have a common factor of x[sup:2c8nk5jr]2[/sup:2c8nk5jr], and the last two terms have a common factor of 2.

Remove the greatest common factor from each pair of terms:

x[sup:2c8nk5jr]2[/sup:2c8nk5jr](x - 1) + 2(x - 1)

Now, do you see that (x - 1) is a factor of each term? Remove it, and you have

(x - 1)(x[sup:2c8nk5jr]2[/sup:2c8nk5jr] + 2)

Your original expression is factored...to make sure it is COMPLETELY factored, examine the expressions inside the parentheses to see if either or both of them can be factored further. If they can't be, you're done.
 
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