Cracking The SAT Premium

Here is an example:

Problem: If 2x = –1, then (2x − 3)^2 = ?

Solution: Don’t solve for x; simply plug in –1 for 2x, like this:

(2x −   3)^2    =   (–1 –   3)^2

                                            =   (–4)^2

                        =   16

Solving Quadratic Equations

To solve quadratic equations, remember everything you’ve learned so far: Look for direct solutions and
either factor or expand when possible.

Here’s an example:

If  (x  +   3)^2    =   (x  −   2)^2 ,  what    is  the value   of  x   ?

Here’s How to Crack It

Expand both sides of the equation using FOIL:

(x  +   3)(x    +   3)  =   x^2     +   6x  +   9

(x  −   2)(x    −   2)  =   x^2     –   4x  +   4

x^2     +   6x  +   9   =   x^2     –   4x  +   4

Now you can simplify. Eliminate the x^2 terms, because they are on both sides of the equal sign. Now you
have 6x + 9 = – 4x + 4, which simplifies to

10 x    =   –5

x   =   –

Factoring Quadratics

To solve a quadratic, you might also have to factor the equation. Factoring a quadratic basically involves
doing a reverse form of FOIL.

For example, suppose you needed to know the factors of x^2 + 7x + 12. Here’s what you would do:

1. Write down 2 sets of parentheses and put an x in each one because the product of the first terms