The Quadratic Equation - Factoring Method

The quadratic equations is a topic under the series of algebra. quadratic equation is a polynomial of second degree.

quadratic equation is a popular topic in mathematics.

Quadratic equation is of the form ax*2+bx+c =0

Where a is the co-efficient of x raise to the power of 2
in the quadratic equation

b is the co-efficient of x in the quadratic equation

While c is a constant in the quadratic equation.

An example of a quadratic equation is:

X*2 + 3X + 2.=0

The quadratic equations can be solved by one of the following methods:

1. Factoring method
of solving quadratic equation

2. Completing the square method
of solving quadratic equation

3. Graphical method of solving quadratic equation

4. Formular method of solving quadratic equation

Factoring method of solving quadratic equation is more of elementary methods of solving quadratic equations and it is easy to use .
It involves taking factors of the quadratic equation by multiplication of cofiecient of X(square i.e ,a) in the quadratic equation and C (which is a constant) in the quadratic equation and try to bring out a combination such that when added or subtracted will result in co-efficient of X( raise to the power of 1)in the quadratic equation as in AX*2 + BX + C =0
which is the prototype of our quadratic equations

Let us take a typical example of the quadratic equation we have been discussing above

Question: Solve by factorisation method the quadratic equation X*2 + 3X + 2=0

Solution:
compare the quadratic equation X*2 + 3X + 2=0 to it's prototype quadratic equations AX*2 + BX + C =0
Where A=+1
in our quadratic equations example
B=+3
in our quadratic equation example
C=+2 in our quadratic equation example
As in the coefficients of our quadratic equation prototype when compared.

Now multiply +2 and +1(obtained from our quadratic equation example) (multiplying A and C)
The result is +2
Factors of +2 include +2 and +1 it could also be -2 and -1 because when multiply wa still arrive at +2

now that we have our factors for our quadratic equation,

we will re-write the quadratic equation as

x*2 + 2X + X + 3=0

Note that 2X + X = 3X

So that no mathematical rule is violated or value changed in our quadratic equation.

The quadratic equation x*2 + (2X + X) + 3 Is still the same as quadratic equation x*2 + 3X + 3

If we decide to group our quadratic equation x*2 + 2X + X + 3=0

we would then have:
(X*2 + 2X)+(X+2)=0
X(X+2) + 1(X+2)=0
(X+1)(X+2)=0

i.e. Either (X+2) or (X+1) = 0
X+2 =0, or X+1=0.
X=-2 or X=-1

Factorisation method of solving quadratic equation has previously said, is more of elementary method in solving quadratic. Some other quadratic equations may not moveable by factoring method of quadratic equation so we can employ other methods of solving quadratic equation like the

Completing the square method of solving quadratic equation,graphical method quadrtic equation, or formula method of solving quadratic equation.