and 4. Since 12 is positive and k is negative, then you’ll need subtraction signs in both factors.
The possibilities are as follows:
x^2 + kx + 12 = (x – 1)(x − 12)x^2 + kx + 12 = (x − 2)(x − 6)x^2 + kx + 12 = (x − 3)(x − 4)If you FOIL each of these sets of factors, you’ll get the following expressions:
(x − 1)(x − 12) = x^2 – 13x + 12(x − 2)(x − 6) = x^2 – 8x + 12(x − 3)(x − 4) = x^2 – 7x + 12The correct answer is (A), as −13 is the only value from above included in the answers. Of course, you
didn’t need to write them all out if you started with 1 and 12 as your factors.
SAT Favorites
The test writers play favorites when it comes to quadratic equations. There are three equations that they
use all the time. You should memorize these and be on the lookout for them. Whenever you see a quadratic
that contains two variables, it is almost certain to be one of these three.
(x + y)(x − y) = x^2 – y^2
(x + y)^2 = x^2 + 2xy + y^2
(x − y)^2 = x^2 – 2xy + y^2Here’s an example of how these equations will likely be tested on the SAT. Try it:
11.If 2x − 3y = 5, what is the value of 4x^2 – 12xy + 9y^2 ?
A)
B) 12
C) 25
D) 100