This is a free lesson from our course in Algebra II
In this section you will learn the process of factoring as a method to solve quadratic equations. Quadratic equations are the equations
that contain a power of two as the highest power in the equation.
Factoring a quadratic equation means breaking the quadratic back into its binomial parts. Simply saying the factoring of
x^{2} + ( a + b )x + ab
will result into ( x + a) ( x + b ).For example, the two factors of x^{2} + 12x + 35 are ( x + 5 )( x + 7 ). Many of the simpler quadratic equations with rational roots can be solved by factoring.
(More text below video...)
(Continued from above)
Using the fact that a product is zero if any of its factors is zero you follow these steps :
• bring all terms to the left and simplify, leaving zero on the right side.
• factorize the quadratic expression.
• set each factor equal to zero.
• solve the resulting linear equations.
• check the solutions in the original equation.
For example, find the solution of the quadratic equation x^{2} = 12x + 35.
x^{2}  12x – 35=0.
(x^{2}+ 12x + 35)=0
(x^{2}+ 12x + 35)=0
(x+7)(x+5)=0
x+7=0 & x+5=0
so, x = 7 and x = 5.
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