How to factor? Are you scared of factor? Do you face trouble while doing these math’s? They are not as hard as you think and since they are a part of algebra you will understand it once you start practicing. Let us start with knowing what is a factor. You are definitely familiar with the times table such as 3 X 3 = 9 or 4 X 3 = 12. The 3 and 4 are factors and the result is the product (9 and 12). It is a whole number that divides precisely into another number. Here are the whole numbers: 1, 2, 4, 8 and not 3 or 5.
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Five or three are not whole numbers because you cannot divide them equally unlike the other numbers. Suppose, there are four sweets. You can divide them equally between two people. Two for each and you can divide the four sweets among four people and again equally. Therefore, you can say.
2 x 2 = 4
4 x 1 =4
The factors are 2, 1 and 4.
Let us factor second degree polynomials. The format is ax2 + bx + c = 0
Rearrange your equation with the smallest one at the beginning such as 3 + 3x2 + 11x = 0
For example, you have an equation x²+ x + 12
x² + 4x – 3x +12
x(x+4) -3(x+4)
(x+4) (x-3) are factors.
Here is how you do it. First of all, look at the numbers. Arrange them and make sure there is no number on the other side, that means on the other side it should be zero. If the equation was x²+3x+12= -3x, rearrange them and make them as small as possible. It will be x²+ 3x+ 3x+ 12 =O, later add the two 3x and your final equation is x²+6x+12 as you have shortened it out, it is now ready to have its factors.
For the previous equation, if you had a zero at the end with an equal sign, you would have to find the value of the x. Then, the result would be x= -4 and x =3. Here is how you do it.
(x=4)(x-3)
x + 4 = 0 & x-3=0
x = -4 x= 3
Let us see how we got the 4 and 3. We look at the single number of the equation that does not have any x with it. In this case, it is the 12. Go through the times tables and think which numbers that can be multiplied to get 12 and also be added or subtracted to get 1. We know,
6 x 2 = 12
3 x 4 = 12
12 x 1 = 12
Adding or subtracting 6 and 2 will never get you 1 neither will 12 and 1. It is clear that 4 and 3 can be subtracted to get 1.
In case of simple equations, you will be able to figure it out yourself with just looking at it. For example, 4x²+ 4x+1 will result in (2x + 1) (2x +1) when you try to factor it.
