Date: Thu, 25 Mar 1999 18:45:51 -0800 (PST) Sender: Maggie Subject: help me please
I don't know anything about factoring would you plese help me.
54x
125-8x
12x
9 - 81x
a I would greatly appreciate any help you can give me thanks. Hi Maggie
Remember that factoring is the process of unmultiplying. When you want to factor 6 you want to know what numbers can multiply to give 6. (You can have the obvious one [1x6] and another one [3x2].)
## FACTORING BY NUMBERS- Count the number of terms.
- Look for a common factor.
- Look again!
- If there are TWO terms then it is probably:
- difference of (two) squares
- difference of (two) cubes
- sum of (two) cubes.
- If there are THREE terms then it is probably a trinomial
(the exponent of the middle term will be one half of the
exponent of the first and/or third term).
- If there are FOUR OR MORE terms then it is probably grouping.
## FACTOR THEOREM## If f(x) is a polynomial and f(a) = 0 then x - a is a factor of f(x).The Factor Theorem can be used almost any time.
## YOUR PROBLEMSLet's look at3x.
^{4} - 48There are 2 terms.
Now we look to see if there is any number or variable that is common to both terms. We see that each term is divisible by 3 and so we know that 3 is a common factor. We can get the other factor by dividing (3x We have factored the expression and so can say that we are finished, however if we were asked to "factor completely" then we need to check to see if the expression in the brackets can be factored further. (E.g. 30 = 2x15 = 2x3x5.)
So let's look at x
Start the process again. There are 2 terms and there is nothing common to the 2 terms. There are 2 terms separated by a - sign so it might be difference of squares or difference of cubes. Notice that both x
Recall that a You can verify this by multiplying.
Now we know that 3x If we were told to factor completely then we must check the two expressions in the brackets to see if they can be factored further.
Look at x
There are 2 terms and nothing is common.
So x
Now look at x Finally we know that
3x
Now let's try
There are 2 terms and there is a common factor of 2.
Then the expression in the brackets is the difference of 2 cubes. Remember how to factor a
a
Now
There are 3 terms and 3 is common.
So 12x Now check the part in the brackets. There are 3 terms and nothing is common and so it might be a trinomial. It is and can be factored by whatever method you use for factoring trinomials. (I don't want to give you a different method than the one that you are currently using.)
The key here is to realize that there are only 2 terms and there is nothing common and so it must be the sum of 2.... Factoring is both an art and a science. I find that the checklist helps with the science but you do need to look at each new expression with fresh eyes.
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