INPUT ARTICLE: Article: Factoring is conceptually simple, but, in practice, can prove to be challenging when applied to complex equations. Because of this, it's easiest to approach the concept of factoring by starting with simple numbers, then move on to simple equations before finally proceeding to more advanced applications. A given number's factors are the numbers that multiply to give that number. For example, the factors of 12 are 1, 12, 2, 6, 3 and 4, because 1 × 12, 2 × 6, and 3 × 4 all equal 12.  Another way to think of this is that a given number's factors are the numbers by which it is evenly divisible. Can you find all the factors of the number 60? We use the number 60 for a wide variety of purposes (minutes in an hour, seconds in a minute, etc.) because it's evenly divisible by a fairly wide range of numbers. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Just as lone numbers can be factored, so too can variables with numeric coefficients be factored. To do this, simply find the factors of the variable's coefficient. Knowing how to factor variables is useful for simplifying algebraic equations that the variables are a part of. For example, the variable 12x can be written as a product of the factors of 12 and x. We can write 12x as 3(4x), 2(6x), etc., using whichever factors of 12 are best for our purposes. We can even go as far as to factor 12x multiple times. In other words, we don't have to stop with 3(4x) or 2(6x) - we can factor 4x and 6x to give 3(2(2x) and 2(3(2x), respectively. Obviously, these two expressions are equal. Using your knowledge of how to factor both lone numbers and variables with coefficients, you can simplify simple algebraic equations by finding factors that the numbers and variables in an algebraic equation have in common. Usually, to make the equation as simple as possible, we try to search for the greatest common factor. This simplification process is possible because of the distributive property of multiplication, which states that for any numbers a, b, and c, a(b + c) = ab + ac.  Let's try an example problem. To factor the algebraic equation 12 x + 6, first, let's try to find the greatest common  factor of 12x and 6. 6 is the biggest number that divides evenly into both 12x and 6, so we can simplify the equation to 6(2x + 1). This process also applies to equations with negatives and fractions. x/2 + 4, for instance, can be simplified to 1/2(x + 8), and -7x + -21 can be factored to -7(x + 3).

SUMMARY: Understand the definition of factoring when applied to single numbers. Understand that variable expressions can also be factored. Apply the distributive property of multiplication to factor algebraic equations.


INPUT ARTICLE: Article: You can choose from all sorts of hairstyles to wear in the gothic scene. For a feminine look, get your hair cut into a bob of shoulder or chin length. You could also sport a cute pair of double buns or braids. Great masculine hairstyles include undercuts and mohawks. You’re already wearing black clothing, so black hair could make you look monotonous. Neon colored hair is common in goth fashion, especially in shades of white, grey, green, purple, pink, blue, and red. Natural hair colors work just as well in goth fashion. Consider going with dark brown, a soft shade of light brown, or platinum blond. A septum piercing goes through the center of your nostrils. You can recognize it as a hoop going through both nostrils, sort of like a bull. Septum piercings have become popular in the goth scene, and can be adorned with a wide variety of jewelry. Hoops with swirled or star-shaped ornaments are most common. If you aren’t comfortable getting a real septum piercing, you can wear a false piercing instead. Tattoos have always been part of the goth style, so now is the perfect chance to get one if you aren’t tattooed already. Any location and style is fine. Birds, roses, pentagrams, skulls, and other macabre images are the most popular styles. Be sure to wear clothing that puts your tattoos on display, such as short-sleeved tops or black denim/leather shorts. Stiletto nails are a type of manicure that features long nails filed into claw shapes. They are a popular choice for a feminine goth style, especially when painted black. If you like, you can add decals shaped like pentagrams, stars, or skulls.

SUMMARY: Get a new haircut or style. Dye your hair neon. Pierce your septum. Get tattooed if you’re 18 or older. Get a stiletto manicure.


INPUT ARTICLE: Article: When you're playing a new opponent, whether it's at a competition or during a friendly game at a family outing, you should assess your opponent's game even while you're warming up. You should look for a few main things: if your opponent is more of an aggressive or defensive player, if his forehand or backhand is his dominant shot, and any weaknesses, such as slow footwork or weak drop shot returns, that you can exploit. Don't hit all of your shots to the same location of the court of your opponent will be able to predict your next move every time. Instead, mix things up by hitting a drop shot followed by a shot to the baseline, or by moving your opponent from the right to the left side of the court. Moving from the front to the back of the court is particularly tricky unless your opponent has very nimble feet. Many players are weaker on the backhand side, so try shooting toward your opponent's backhand and see if this makes your opponent return less shots. If so, continue to exploit your opponent's backhand. Your backhand is the left side for right-handed players and the right side for left-handed players. When you're up at the net, simply hit the shuttle short, just barely over to your opponent's side. This will make your opponent run and will catch him off guard. This is a great technique if your opponent is positioned near the back line. If your opponent knows that you are going to do a short shot, you need to flick the shuttle over the opponent or to another side and if you didn't do this, your opponent will fly the shuttle near the back line. If your opponent hits the shuttle straight at you, hit the shuttle in a different direction instead of hitting it right back at your opponent, where he will expect it to go. This will work especially well if the shuttle has generated a lot of momentum. If you're quick on your feet, you can change the direction of the shuttle and not give your opponent enough time to react to a fast-moving shuttle. If you have mastered the drop shot, then use it to make your opponent run all the way to the front of the court. Then return the next shot all the way to the back of the court. Not only will this force your opponent to be quick on his feet, but it will also catch him off guard. This is also a great way to tire your opponent. To do a drop shot, hit the shuttle lightly so it just crosses the net. If you like staying near the net, serve short, hit drop shots, and do whatever you can to make sure that your opponent can't hit the shuttle to the back line. If you're more comfortable at the back line, then serve long and hit speedy long shots so your opponent doesn't have a chance to move you toward the net. Make the opponent lose all control as you play your style of game and maximize your strengths.

SUMMARY:
Understand your opponent's game. Make your opponent move around the court. Shoot toward your opponent's backhand. Hit a simple short shot. Change the direction of the shuttle. Hit a drop shot followed by a shot to the back of the court. Make your opponent play your style of game.