GMAT Quantitative Review

3.0 Math Review

3.2 Algebra

5. Solving Equations by Factoring

Some equations can be solved by factoring. To do this, first add or subtract expressions to bring all the expressions to one side of the equation, with 0 on the other side. Then try to factor the nonzero side into a product of expressions. If this is possible, then using property (7) in section 3.1.4 (“Real Numbers”) each of the factors can be set equal to 0, yielding several simpler equations that possibly can be solved. The solutions of the simpler equations will be solutions of the factored equation. As an example, consider the equation image:

image.

For another example, consider image. A fraction equals 0 if and only if its numerator equals 0. Thus, image:

image

But image has no real solution because image for every real number. Thus, the solutions are 0 and 3.

The solutions of an equation are also called the roots of the equation. These roots can be checked by substituting them into the original equation to determine whether they satisfy the equation.