Factoring a quadratic equation
means expressing it in two brackets. A quadratic equation is one in the form ax2
+bx+c = 0.
Factoring when a = 1
Firstly, make sure the equation
is in the standard format, as above. Then, to make things easier for you, write down the two brackets -
( x )( x ) = 0.
Now, you need to find two numbers that multiply to give c, and add/subtract to give the coefficient of b. Then you simply put these numbers into the brackets, and sort out the +/- signs correctly.
x2 + x = 12
First, we rearrange into the standard format-
x2 - x - 12 = 0
We need two pairs of numbers hat multiply to give 12 and add/subtract to give 1. The numbers are clearly 3 and 4.
Now, write the equation -
(x + 3)(x - 4) = 0
Then, as an essential check, we'd expand the brackets.
Factoring when a does not equal 1
3x 2 + 7x + 6 = 0
The method is the same is pretty much the same as before. In this case we'd have to find two numbers that multiply with the 3x and x terms in the brackets and then add or subtract to give the value of b. So in this case it'd be 2 in the first bracket and 3 in the second.