Quadratic Factoring

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Quadratic means square. The equation which has the highest degree for the variable as two is called a quadratic equation. So the degree of the polynomial for a quadratic equation is always 2. The general form of a quadratic equation is ax2 + b x + c = 0. Here x is the unknown variable and a. b. c are the constants. Factoring is a very useful method used to solve any quadratic equation. Given below are examples of solving a quadratic equation using factorization.

Example 1: Solve the quadratic equation x2 + 6x + 5 = 0.

Solution: Given here is the quadratic equation x2 + 6x + 5 = 0.

The first step is to write 6 x = 5 x + x.

The equation can be written as x2 + 5x + x + 5 = 0

Now factoring the common terms gives x(x + 5) + 1(x + 5) = 0.

Hence (x + 5) (x + 1) = 0

Therefore, x = -5, -1 are the solutions.
 
Example 2: Solve the quadratic equation x2 - 8x - 9 = 0.

Solution: Given here is the quadratic equation x2 -8x - 9 = 0.

The first step is to write -8 x = -9 x + x.

The equation can be written as x2 – 9 x + x - 9 = 0

Now factoring the common terms gives x(x - 9) + 1(x - 9) = 0.

Hence (x - 9) (x + 1) = 0

Therefore, x = 9, -1 are the solutions.

 
 

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