Factor
To factor an expression, take out the factors common to all terms in the expression.
Simplify: 6 ab + 3a
SOLUTION: Each term has 3a as a factor. To see this, rewrite the expression as
3 a × 2b + 3a × 1. Take 3a out of each term and arrive at 3a(2b + 1).
Simplify: 4 x^2 + 3x
SOLUTION: Each term shares a factor of x. Take x out of each term and arrive
at x(4x + 3)
Basic Equations and Solving for a Variable
Whenever two expressions are set equal to each other, you have an equation:
7 × 6 = 14 × 3
The fundamental rule for all equations is the following: you can perform any
operation on an equation as long as you perform that operation on both sides.
In the preceding example, if you divide both sides by 3, you will end up with
7 × 2 = 14. While the values on both sides of the equation changed, the equation
itself is still true.
In algebra, equations will have variables, which are letters used to represent
some unknown quantity in an equation.
If 3x + 2 = 14, then x =?
When asked to solve for a variable, your goal will be isolate the variable by
undoing the operations done to that variable. To do so, you are going to use
PEMDAS, but in reverse!
3 x + 2 = 14 1. Get rid of the addition by subtracting 2 from
both sides.
3 x + 2 − 2 = 14 – 2
3 x = 12 2. Get rid of the multiplication by dividing both
sides by 3.
33 x =^123
x = 4
260 PART 4 ■ MATH REVIEW
03-GRE-Test-2018_173-312.indd 260 12/05/17 11:53 am