Factoring Special Cases

What is a Plant Cell? Plant cells are eukaryotic cells that vary in several fundamental factors from other eukaryotic organisms. Both plant and animal cells contain a nucleus along with similar organelles. One of the distinctive aspects of a plant cell is the presence of a cell wall outside the cell membrane. Plant Cell Structure Just like different organs within the body, plant cell structure includes various components known as cell organelles that perform different functions to sustain itself. These organelles include: Cell Wall It is a rigid layer which is composed of polysaccharides cellulose, pectin and hemicellulose. It is located outside the cell membrane. It also comprises glycoproteins and polymers such as lignin, cutin, or suberin. The primary function of the cell wall is to protect and provide structural support to the cell. The plant cell wall is also involved in protecting the cell against mechanical stress and providing form and structure to the cell. It also filters the molecules passing in and out of it. The formation of the cell wall is guided by microtubules. It consists of three layers, namely, primary, secondary and the middle lamella. The primary cell wall is formed by cellulose laid down by enzymes. Cell membrane It is the semi-permeable membrane that is present within the cell wall. It is composed of a thin layer of protein and fat. The cell membrane plays an important role in regulating the entry and exit of specific substances within the cell. For instance, cell membrane keeps toxins from entering inside, while nutrients and essential minerals are transported across. Nucleus The nucleus is a membrane-bound structure that is present only in eukaryotic cells. The vital function of a nucleus is to store DNA or hereditary information required for cell division, metabolism and growth. 1. Nucleolus: It manufactures cells’ protein-producing structures and ribosomes. 2. Nucleopore: Nuclear membrane is perforated with holes called nucleopore that allow proteins and nucleic acids to pass through. Plastids They are membrane-bound organelles that have their own DNA. They are necessary to store starch and to carry out the process of photosynthesis. It is also used in the synthesis of many molecules, which form the building blocks of the cell. Some of the vital types of plastids and their functions are stated below: Leucoplasts They are found in the non-photosynthetic tissue of plants. They are used for the storage of protein, lipid and starch. Chromoplasts They are heterogeneous, colored plastid which is responsible for pigment synthesis and for storage in photosynthetic eukaryotic organisms. Chromoplasts have red-, orange- and yellow-colored pigments which provide color to all ripe fruits and flowers. Central Vacuole It occupies around 30% of the cell’s volume in a mature plant cell. Tonoplast is a membrane that surrounds the central vacuole. The vital function of the central vacuole apart from storage is to sustain turgor pressure against the cell wall. The central vacuole consists of cell sap. It is a mixture of salts, enzymes and other substances. Golgi Apparatus They are found in all eukaryotic cells, which are involved in distributing synthesized macromolecules to various parts of the cell. Ribosomes They are the smallest membrane-bound organelles which comprise RNA and protein. They are the sites for protein synthesis, hence, also referred to as the protein factories of the cell. Mitochondria They are the double-membraned organelles found in the cytoplasm of all eukaryotic cells. They provide energy by breaking down carbohydrate and sugar molecules, hence they are also referred to as the “Powerhouse of the cell.” Lysosome Lysosomes are called suicidal bags as they hold digestive enzymes in an enclosed membrane. They perform the function of cellular waste disposal by digesting worn-out organelles, food particles and foreign bodies in the cell. In plants, the role of lysosomes is undertaken by the vacuoles. Chloroplasts It is an elongated organelle enclosed by phospholipid membrane. The chloroplast is shaped like a disc and the stroma is the fluid within the chloroplast that comprises a circular DNA. Each chloroplast contains a green colored pigment called chlorophyll required for the process of photosynthesis. The chlorophyll absorbs light energy from the sun and uses it to transform carbon dioxide and water into glucose. Structure of Chloroplast Chloroplasts are found in all higher plants. It is oval or biconvex, found within the mesophyll of the plant cell. The size of the chloroplast usually varies between 4-6 µm in diameter and 1-3 µm in thickness. They are double-membrane organelle with the presence of outer, inner and intermembrane space. There are two distinct regions present inside a chloroplast known as the grana and stroma. • Grana are made up of stacks of disc-shaped structures known as thylakoids or lamellae. The granum of the chloroplast consists of chlorophyll pigments and are the functional units of chloroplasts. • Stroma is the homogenous matrix which contains grana and is similar to the cytoplasm in cells in which all the organelles are embedded. Stroma also contains various enzymes, DNA, ribosomes, and other substances. Stroma lamellae function by connecting the stacks of thylakoid sacs or grana. The chloroplast structure consists of the following parts: Membrane Envelope It comprises inner and outer lipid bilayer membranes. The inner membrane separates the stroma from the intermembrane space. Intermembrane Space The space between inner and outer membranes. Thylakoid System (Lamellae) The system is suspended in the stroma. It is a collection of membranous sacs called thylakoids or lamellae. The green colored pigments called chlorophyll are found in the thylakoid membranes. It is the sight for the process of light-dependent reactions of the photosynthesis process. The thylakoids are arranged in stacks known as grana and each granum contains around 10-20 thylakoids. Stroma It is a colorless, alkaline, aqueous, protein-rich fluid present within the inner membrane of the chloroplast present surrounding the grana. Grana Stack of lamellae in plastids is known as grana. These are the sites of conversion of light energy into chemical energy. Chlorophyll It is a green photosynthetic pigment that helps in the process of photosynthesis. Functions of Chloroplast Following are the important chloroplast functions: • The most important function of the chloroplast is to synthesize food by the process of photosynthesis. • Absorbs light energy and converts it into chemical energy. • Chloroplast has a structure called chlorophyll which functions by trapping the solar energy and is used for the synthesis of food in all green plants. • Produces NADPH and molecular oxygen (O 2 ) by photolysis of water. • Produces ATP – Adenosine triphosphate by the process of photosynthesis. • The carbon dioxide (CO2) obtained from the air is used to generate carbon and sugar during the Calvin Cycle or dark reaction of photosynthesis. Mitochondria “Mitochondria are membrane-bound organelles present in the cytoplasm of all eukaryotic cells, that produce adenosine triphosphate (ATP), the main energy molecule used by the cell.” What are Mitochondria? Popularly known as the “Powerhouse of the cell,” mitochondria (singular: mitochondrion) are a double membrane-bound organelle found in most eukaryotic organisms. They are found inside the cytoplasm and essentially function as the cell’s “digestive system.” They play a major role in breaking down nutrients and generating energy-rich molecules for the cell. Many of the biochemical reactions involved in cellular respiration take place within the mitochondria. The term ‘mitochondrion’ is derived from the Greek words “mitos” and “chondrion” which means “thread” and “granules-like”, respectively. It was first described by a German pathologist named Richard Altmann in the year 1890. Structure of Mitochondria • The mitochondrion is a double-membraned, rod-shaped structure found in both plant and animal cell. • Its size ranges from 0.5 to 1.0 micrometers in diameter. • The structure comprises an outer membrane, an inner membrane, and a gel-like material called the matrix. • The outer membrane and the inner membrane are made of proteins and phospholipid layers separated by the intermembrane space. • The outer membrane covers the surface of the mitochondrion and has a large number of special proteins known as porins. Cristae The inner membrane of mitochondria is rather complex in structure. It has many folds that form a layered structure called cristae, and this helps in increasing the surface area inside the organelle. The cristae and the proteins of the inner membrane aid in the production of ATP molecules. The inner mitochondrial membrane is strictly permeable only to oxygen and ATP molecules. A number of chemical reactions take place within the inner membrane of mitochondria. Mitochondrial Matrix The mitochondrial matrix is a viscous fluid that contains a mixture of enzymes and proteins. It also comprises ribosomes, inorganic ions, mitochondrial DNA, nucleotide cofactors, and organic molecules. The enzymes present in the matrix play an important role in the synthesis of ATP molecules. Functions of Mitochondria The most important function of mitochondria is to produce energy through the process of oxidative phosphorylation. It is also involved in the following process: 1. Regulates the metabolic activity of the cell 2. Promotes the growth of new cells and cell multiplication 3. Helps in detoxifying ammonia in the liver cells 4. Plays an important role in apoptosis or programmed cell death 5. Responsible for building certain parts of the blood and various hormones like testosterone and estrogen 6. Helps in maintaining an adequate concentration of calcium ions within the compartments of the cell 7. It is also involved in various cellular activities like cellular differentiation, cell signaling, cell senescence, controlling the cell cycle and in cell growth. Disorders Associated with Mitochondria Any irregularity in the way mitochondria function can directly affect human health, but often, it is difficult to identify because symptoms differ from person to person. Disorders of the mitochondria can be quite severe; in some cases, they can even cause an organ to fail.

Factoring special polynomials

Factoring polynomials (special product)

SPECIAL PRODUCTS AND FACTORING

Assessment on Special Products and Factoring - Starter Quiz

Short Quiz in Math 8 Special Products and Factoring

Multiple choice quiz on this reading: By 1900, the United States had claimed its place as a world power through the Spanish-American War. As the new century began, the country governed subject territories in Puerto Rico, Hawaii, Guam, the Wake Islands, and the Philippines. U.S. troops also occupied Cuba. U.S. businesses reached beyond the country's borders. During the first decade of the new century, the Coca-Cola Company, Quaker Oats, AT&T, the Standard Oil Company, Du Pont, General Electric, and Ford Motor Company seized the opportunity for international sales. After finding international markets, they built factories abroad, taking advantage of lower labor costs in foreign countries. Then they asked for U.S. protection of their investments and interests. Foreign countries invested heavily in Central America. U.S. investors focused on banana plantations and mining, as well as railroads, with little money in government bonds. By 1913, U.S. investments in Central America totaled about $93 million. British investment in Central America peaked at about $115 million in 1913. About $75 million of that total represented railroad holdings, mostly in Costa Rica and Guatemala. The other $40 million was in government bonds, which were worth little or nothing. The Roosevelt Corollary to the Monroe Doctrine From its earliest days, the United States claimed a special interest in the Western Hemisphere. The Monroe Doctrine, issued in 1823, warned European powers to keep their hands off Latin America. In 1902, Britain, Germany, and Italy mounted a naval blockade of Venezuela. They wanted to force the government to repay its debts. All the countries involved eventually agreed to settle the matter by arbitration. The United States stood back and did nothing, but U.S. citizens were clearly uneasy with the appearance of European military forces in "their" hemisphere. In 1904, President Theodore Roosevelt issued a corollary to the Monroe Doctrine, saying that the United States would act as a police officer to keep order in the region. He intended both to keep European military forces out of the hemisphere and to protect U.S. and European investors, exerting whatever pressure or control on Latin American governments that might be necessary to these ends. In 1905, the Dominican Republic owed $40 million in debts to European lenders. In order to prevent the European nations from using military force to collect their debts, Roosevelt used U.S. power. The United States basically took over collection of Dominican customs taxes, declared that $20 million of the debt was unjustified, and began repayment of the rest. Building a Canal The United States needed a canal through Central America, in order to save shipping time and costs. Colombia had the best location for a canal, and the United States negotiated a deal. It would pay Colombia $10 million for a three-mile-wide strip of land and would make annual rental payments of $250,000 yearly, beginning in 1912. Colombia's Senate turned down the deal, and Roosevelt exploded in rage, calling its members "foolish and homicidal corruptionists." Roosevelt considered seizing the land for the canal by military force but soon found an easier way. The province of Panama seceded from Colombia. A U.S. gunship stood off shore, protecting the Panamanian rebels. They formed a new republic under the protection of the United States. The new country of Panama and the United States agreed on a canal treaty within days. The new treaty had similar terms except that the Canal Zone would be five miles wide, instead of three, and the United States would guarantee and maintain the independence of Panama. Revolutions While Roosevelt welcomed the revolution that separated Panama from Colombia, he opposed most other revolutionary activity. So did his successors in office, William Howard Taft and Woodrow Wilson. The U.S. presidents sent troops to put down revolutions in Nicaragua and Haiti, using U.S. military forces to set up new governments in those countries and maintaining military occupations for years. U.S. military interventions were frequent throughout the hemisphere. Dollar Diplomacy President Taft preferred using "dollar diplomacy" to control Latin American countries. In Honduras, for example, U.S.-based banana companies virtually ran the government. Taft supported expanded U.S. investment in South and Central American countries, the Caribbean, and the Far East. He ordered Secretary of State Philander Chase Knox to protect U.S. investments, sending in military troops if necessary. On the World Stage As a world power, the United States did not limit its involvement to the Western Hemisphere. In 1905, President Roosevelt brought Russia and Japan to the negotiating table to end their war over control of Korea and Manchuria. Roosevelt agreed to Japanese annexation of Korea in return for Japan giving up any claim to China, Hawaii, and the Philippines. Roosevelt won the Nobel Peace Prize for settling this dispute. In 1906, Roosevelt's negotiating powers were tested again. This time, he mediated a dispute between the Alliance powers—Germany, Austria-Hungary, and Italy—with the Entente—France, Russia, and Britain—over control of Morocco. The United States backed France and ended the dispute. No longer an upstart, the United States had taken its place as a world power alongside its former colonial ruler.

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