# SAT Math: Algebra

## Equations

If n and k are constants and x2 + kx + 12 is equivalent to (x - 4)(x + n), what is the value of k?

A.  -7

B.  -4

C.  -3

D.  4

E.  7

## Knowsys Method

Read the question carefully.  Many students will see the word "is equivalent" and set up the problem without thinking about the fact that the second value shows the binomial factors of the equation.  If you realize that these are the factors, you can solve the problem very quickly.

Identify the bottom line.  k = ?

Assess your options.  You could work backwards from the answer problems, but you may have to work the problem more than once.  Instead, use your knowledge of equations to solve the problem.

Attack the problem.  You may be tempted to look at the plus signs and think that your answer must be positive, but think more carefully about the variables n and k.  You do not know whether they are positive or negative!  Adding a negative number is the same thing as subtracting a number.

x2 + kx + 12 is the equation and it is factored as (x - 4)(x + n). When you factor something, the last two numbers inside the parentheses must multiply to equal the last number in your equation. That means that -4n = 12. You now know that n = -3.

Now you can write your factors as (x - 4)(x - 3) by plugging in -3 for n.  You could FOIL these factors to get a polynomial and find out what k would be, but think about it again.  The last two numbers inside the parentheses must add to create the number of the middle term in your polynomial.  So -3 + -4 = k.  Therefore, k = -7.