McGraw-Hill Education GRE 2019

So stick to the following rule: Set quadratic equations equal to zero. Let’s redo

the preceding example:

4 x^2 = x

Step 1: Subtract x from both sides: 4x^2 − x = 0.

Step 2: Factor x from both terms: x(4x − 1) = 0.

Step 3: Solve for x.

Since you have a product set equal to zero, either:

x = 0 or 4x − 1 = 0

↓

4 x = 1

x =^14

Expanding a Quadratic: FOIL

So far, you have looked at situations where you have taken quadratic equations

in their expanded form and put them into factored form. Sometimes, you will be

expected to go in the opposite direction: from factored form to expanded form.

To do so, you will want to use an acronym that you may remember from high

school: FOIL.

FOIL stands for:

First

Outer

Inner

Last

To expand the expression (x + 3)(x − 5), do the following:

First: Multiply the first term in each parentheses together: (x)(x) = x^2

Outer: Multiply the first term in the first parentheses by the last term in the

second parentheses: x(−5) = −5x

Inner: Multiply the inner terms of the product together: 3(x) = 3x

Last: Multiply the last term in each set of parentheses together: 3(5) = –15

Now you have an expression with four terms: x^2 − 5x + 3x + 15. Group like

terms, and you will arrive at the quadratic: x^2 − 2x + 15.

CHAPTER 11 ■ ALGEBRA 285

03-GRE-Test-2018_173-312.indd 285 12/05/17 11:55 am