Factorization is the decomposition of an object (number, polynomial, and matrix,etc). It is an important way of finding answer(s) for a polynomial. It also helps with simplification of polynomials. A well developed factoring skill will help you answering algebra questions faster, but a lot of high school students are having problems with it.
Here are some basic tips that will help you to factor faster.
1. Always start with real numbers:
Students are more familiar with calculations with real number than variables, so working with real number will reduced the the amount of calculation and chance of making mistakes.
For example (100x+50)/(60x+60) can be reduced to (2x+1)/(x+1), the polynomial looks much more elegant and it is easier to calculate.
2. Recognize common terms:
Here is some common terms that you should remembered:
1.) (a+b)^2=a^2+2ab+b^2
2.) (a-b)^2=a^2-2ab+b^2
3.) a^2-b^2=(a+b)(a-b)
4.) a^3-b^3=(a-b)(a^2+ab+b^2)
5.) a^3+b^3=(a+b)(a^2-ab+b^2)
If you can remember the formula above, you will be able to factor in a much faster speed.
3. cross multiplication
A lot of the questions we have will not give you an easy polynomial so that you can solve by one of the formula above.There is another tool called cross multiplication that will be helpful.(This is assume we are working with whole number)
For example:
x^2+2x-3
Clearly you can not apply above formulas to this polynomial, but if you think about the factor form for this polynomial, it has to be in the form of (ax+b)(cx+d)since X has the exponent of 2. If we expand this we will get acx^2+(ad+bc)x+db. Since ac =1 and a,c are whole numbers we get a=c=1.Sub in a=c=1 we get, d+b =2 ,b*d=-3 we easily get b=3,d=-1 or d=3,b=-1, so the answer will be x^2+2x-3=(x-1)(x+3). In general, if you are given a polynomial in the form of ax^n+bx^m+c, you should start with factoring a and c. You group two factors ( one factor from a and one from c), then you add the product of all the factors , until the sum of the product is b. The factor you get from “a” will be the coefficient for x and the factors from c will be the other number in the bracket.
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This article was written for you by John, one of the tutors with SchoolTutoring Academy.
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