Because there is a remainder, we know that (x – 3) is not a factor of (2x^2 – 5x – 1).
—SamanthaThat’s the process for polynomial long division. This is a tricky topic and will
take some practice to master, particularly if you’re not already a whiz at long
division with numbers. But it’s important to learn because it is likely to appear
on the test in some form.
TRANSFORMATIONS
Finally, the SAT might ask you questions about how altering a function affects
its graph. Here are a few basic transformations that you will want to know:
We’ll take as our basic function y = x^3.
y = x^3 + 5 Graph is shifted up five units
y = x^3 – 5 Graph is shifted down five units
y = (x + 5)^3 Graph is shifted left five units
y = (x – 5)^3 Graph is shifted right five units
y = (2x)^3 Graph is pinched horizontally
y = (½x)^3 Graph is stretched horizontally
y = 2x^3 Graph is stretched vertically
y = ½x^3 Graph is pinched vertically
y = (–x)^3 Graph is reflected over the y-axis
y = –x^3 Graph is reflected over the x-axis
Stretched?! How do you stretch a graph? Well, to your mortal human eyes, it just looks a tad skinnier.
—Samantha