We can only divide by a binomial whose leading coefficient is 1–thus, we must factor the leading coefficient out of the binomial and divide by the leading coefficient separately. Also, the binomial must have degree 1; we cannot use synthetic division to divide by a binomial like x2 + 1.

Answer: In order to divide polynomials using synthetic division, you must be dividing by a linear expression and the leading coefficient (first number) must be a 1. For example, you can use synthetic division to divide by x + 3 or x – 6, but you cannot use synthetic division to divide by x2 + 2 or 3×2 – x + 7.

Synthetic division is another way to divide a polynomial by the binomial x – c , where c is a constant.

1. Step 1: Set up the synthetic division.
2. Step 2: Bring down the leading coefficient to the bottom row.
3. Step 3: Multiply c by the value just written on the bottom row.
4. Step 4: Add the column created in step 3.

Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1. We then multiply it by the “divisor” and add, repeating this process column by column until there are no entries left.

Synthetic Division. Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

The only disadvantage of the synthetic division method is that this method is only applicable if the divisor of the polynomial expression is a linear factor.

Disadvantage: it is only used for dividing polynomial by LINEAR polynomial. In other cases it won’t work….Advantages of this method:

• less space on a paper.
• fewer calculations.
• calculations are made without variables.
• fewer sign errors, because additions are made instead of subtractions (as in long division)

Advantages of Synthetic Division only numbers (not variables) are written down. it uses fewer arithmetic calculations. it is much more compact (taking less horizontal and vertical space) it requires only multiplication and addition, no subtraction (hence is less error-prone)

Paolo Ruffini

If writing as a fraction, the remainder is in the numerator of the fraction and the divisor is in the denominator. For example: Dividing x2+3x−12 by x−3 : When you use Synthetic Division, the answer is x+6 with a remainder of 6.

All you do is multiply and add, which is why synthetic division is the shortcut. The last number, 0, is your remainder. Because you get a remainder of 0, x = 4 is a root.

For the synthetic division method to be possible, the following requirements must be meet: The divisor should be a linear factor. This means that the divisor should be an expression of degree 1. The leading coefficient of the divisor should also be 1.

The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division.

In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials (known as the Ruffini’s rule), but the method can be generalized to division by any polynomial.

The relationship is this: If, when using synthetic division, you divide by a positive and end up with all positive numbers on the bottom row, then the test root is too high. (This does not work in reverse! You can sometimes divide by a too-high test root, but not get all positive numbers on the bottom row!)

You can use long division or synthetic division. Long Division: Step 1: Divide the first term in the numerator by the first term in the denominator, put this in your answer.

Basically the explanation is the fact that we use synthetic division to find factors of polynomials, which essentially is what division is. If the remainder of synthetic division is zero, then the divisor is a factor. The important thing here is that synthetic division only divides a polynomial by a linear factor.

Polynomial long division is a method used to simplify polynomial rational functions by dividing a polynomial by another, same or lower degree, polynomial. In this case, a shortcut method called synthetic division can be used to simplify the rational expression.

And this is the fact you use when you do synthetic division. Make sure you leave room inside, underneath the row of coefficients, to write another row of numbers later. Add down the column: In the synthetic division, I divided by x = –3, and arrived at the same result of x + 2 with a remainder of zero.

: a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.

How to do synthetic division

1. Reverse the sign of the constant term in the divisor. For example, the constant term in the divisor is 5. Change it to -5.
2. Bring down the first coefficient or 1. The 1 will begin the quotient.
3. Multiply the first coefficient by the new divisor and add the answer to the next coefficient or 11. We get 6.

: something resulting from synthesis rather than occurring naturally especially : a product (such as a drug or plastic) of chemical synthesis.

Examples of Synthetic Materials – Examples of synthetic materials include synthetic fibers, ceramics, polymers, artificial foods and medicines, and composites. Synthetic fibers are flexible. They can be used to make clothing and other objects. Some examples of synthetic fibers are rayon, polyester, and nylon.

Synthetic fuels include liquid fuels such as fuel oil, diesel oil, gasoline, and methanol, clean solid fuels, and low-calorific value, medium-calorific value, and high-calorific value gas.

Some examples of synthetic fabrics are polyester, acrylic, nylon, rayon, acetate, spandex, latex and Kevlar. Synthetic fibres are made by the joining of monomers into polymers by the process of polymerization.

5 Examples of Synthetic Fibers

• Polyester. Polyester is a synthetic fiber created from coal and petroleum..
• Rayon. Rayon is a semi-synthetic fiber made from reconstituted wood pulp.
• Spandex. Also known as Lycra or elastane, Spandex is a synthetic fiber characterized by its extreme elasticity.
• Acrylic fibers.
• Microfibers.

Many classes of fiber based on synthetic polymers have been evaluated as potentially valuable commercial products, three of them are nylon, polyester, and acrylic, which dominate the market [20]. There are several methods of manufacturing synthetic fibers, but the most common is the melt-spinning process.

Synthetic paper is a material made out of synthetic resin which is made to have properties similar to regular paper. Synthetic paper is usually made out of either biaxially oriented polypropylene (BOPP) or high-density polyethylene (HDPE). To the polypropylene resin can be added calcium carbonate.

Synthetic paper has grown in popularity for its durability and environmental advantages. This waterproof, tear-resistant plastic prints like its pulp-based counterpart, yet is 100% recyclable.

Environment-friendly solution: Suprabha synthetic paper is biodegradable, and leaves no hazardous traces on the material packaged or in the environment. However, in order to withstand the rigours of outside storage, the product has been designed to resist decomposition for up to a period of five years.

Worksheet Overview Man-made materials are not natural. We dig rocks out of the ground. Paper is made using another material. Remember that the materials we find, without changing them, are natural materials.

Although most people think of glass as a man-made material, it is found in many forms in the natural world. Glass is created when a molten material cools so rapidly that there is not enough time for a crystalline structure to form. …

Wood (natural) being made into paper (man-made). Oil (natural) being made into nylon (man-made). There are a great many man-made substances that we use everyday. Remember if we change them into something else, they are man-made….Well done. Tin is a natural metal.

Wood	Leather	Nylon
Fibreglass	Coal	Sand
Silk	Plastic	Tin

The materials which are made by man are called man made materials. Example: artificial fibres, plastics, glasses are man made materials.

Man-made fibre

• Plastic.
• Rayon.
• Nylon.
• Modacrylic.
• Fibreglass.
• Azlon.
• Metallic fibre.
• Spinneret.

While kerosene can be extracted from coal, oil shale, and wood, it is primarily derived from refined petroleum. Before electric lights became popular, kerosene was widely used in oil lamps and was one of the most important refinery products.

produced, formed, or made by humans. produced artificially; not resulting from natural processes. Textiles. (of a fiber) manufactured synthetically from a cellulosic or noncellulosic base; produced chemically. (of a fabric or garment) constructed of synthetically made fibers.