Consider the equation ax^{2 }+ bx + c = 0. Putting *The* in evidence we get:

Then we can write:

Therefore, the factored form of the equation *ax ^{2 }+ bx + c = 0 is:*

a. (x - x '). (x - x ") = 0 |

Examples:

Write in factored form the equation x

^{2}- 5x + 6 = 0.**Solution:**Calculating the roots of equation x^{2}- 5x + 6 = 0, we get x_{1}= 2 and x_{2}= 3.

Where a = 1, x_{1}= 2 and x_{2}= 3, the factored form of x^{2}- 5x + 6 = 0 can be written as follows: (x-2). (X-3) = 0

Write in factor form the equation 2x

^{2}- 20x + 50 = 0.**Solution**:

Calculating the roots of the 2x equation^{2}- 20x + 50 = 0, we get two real roots equal to 5. Being a = 2, x_{1}= x_{2}= 5, the factored form of 2x^{2}- 20x + 50 = 0 can be written as follows:

2. (x - 5) (x - 5) = 0 or 2. (x - 5)^{2}=0

Write in the factored form the equation x

^{2}+ 2x + 2 = 0.**Solution:**As the , the equation has no real roots.

Therefore, this equation has no factored form in IR.