Degree of a polynomial

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1 Variable Algebra Term Polynomial Monomial Binomial Trinomial Degree of a term Degree of a polynomial Linear

2 A generalization of arithmetic. Letters called variables are used to denote numbers, which are related by laws that hold (or are assumed) for any of the numbers in the set. The four main processes of algebra are (1) simplify, (2) evaluate, (3) factor, and (4) solve. A symbol that represents unspecified elements of a given set. On a calculator, it refers to the name given to a location in the memory that can be assigned a value. An algebraic expression that may be written as a sum (or difference) of terms. Each term of a polynomial contains multiplication only. A number, a variable, or the product of numbers and variables. A polynomial with exactly two terms. A polynomial with one and only one term. The degree of a term is the number of variable factors in the term. If the term has one variable, the degree is the exponent of the variable, or it is the sum of the exponents of the variables if there is more than one variable. A polynomial with exactly three terms. (1) A first-degree polynomial. (2) In one variable, a set of points satisfying the equation Ax 1 B 5 0, A 0. (3) In two variables, a set of points satisfying the equation Ax 1 By 1 C 5 0. The degree of a polynomial is the degree of its highestdegree term.

3 Quadratic Numerical coefficient Like terms (similar terms) Simplify FOIL Common factor Completely factored Differences of squares Spreadsheet Cell

4 Any numerical factor of a term is said to be the coefficient of the remaining factors. The numerical coefficient is the numerical part of the term, usually written before the variable part. In 3x, it is the number 3, in 9x 2 y 3, it is the number 9. Generally, the word coefficient is taken to be the numerical coefficient of the variable factors. (1) A second-degree polynomial. (2) In one variable, a set of points satisfying the equation Ax 2 1 Bx 1 C 5 0, A 0. To simplify a polynomial means to carry out all operations (according to the order-of-operations agreement) and to write the answer in a form with the highest-degree term first, with the rest of the terms arranged by decreasing degree. If there are two terms of the same degree, arrange those terms alphabetically. Terms that differ only in their numerical coefficients. Also called similar terms. A factor that two or more terms of a polynomial have in common. (1) A method for multiplying binomials that requires First terms, Outer terms + Inner terms, Last terms: (a 1 b)(c 1 d) 5 ac 1 (ad 1 bc) 1 bd (2) A method for factoring a trinomial into the product of two binomials. A mathematical expression in the form a 2 2 b 2. An expression is completely factored if it is a product and there are no common factors and no difference of squares that is, if no further factoring is possible. A specific location on a spreadsheet. It is designated using a letter (column heading) followed by a numeral (row heading). A cell can contain a letter, word, sentence, number, or formula. A computer program used to manipulate data and carry out calculations or chains of calculations.

5 Replicating Equation Satisfy Solutions (roots) Solve Equivalent equations Linear equations Quadratic equations Equation properties Symmetric property of equality

6 A statement of equality. On a spreadsheet, the operation of copying a formula from one place to another. The values or ordered pairs of values for which an equation, a system of equations, inequality, or system of inequalities is true. The values that make an open equation true are said to satisfy the equation and are called the solutions or roots of the equation. Two equations with the same solutions. To find the values of the variable that satisfy the equation. An equation of the form ax 2 1 bx 1 c 5 0, a 0. An equation of the form ax 1 b 5 0 (one variable) or Ax 1 By 1 C 5 0 (two variables) A first-degree equation with one or two variables. For example, x and x 1 y are linear. An equation is linear in a certain variable if it is first degree in that variable. For example, x 1 y is linear in x, but not y. If a 5 b, then b 5 a. There are four equation properties: (1) Addition property: Adding the same number to both sides of an equation results in an equivalent equation. (2) Subtraction property: Subtracting the same number from both sides of an equation results in an equivalent equation. (3) Multiplication property: Multiplying both sides of a given equation by the same nonzero number results in an equivalent equation. (4) Division property: Dividing both sides of a given equation by the same nonzero number results in an equivalent equation.

7 Zero-product rule Multiplicity Quadratic formula Comparison property Inequality symbol Inequality Addition property of inequality Multiplication property of inequality Solve an inequality Principle of substitution

8 If a root for an equation appears more than once, it is called a root of multiplicity. For example, (x 2 1)(x 2 1)(x 2 1)(x 2 2)(x 2 2)(x 2 3) 5 0 has roots 1, 2, and 3. The root 1 has multiplicity three and root 2 has multiplicity two. If A B 5 0, then A 5 0 or B 5 0, or A 5 B 5 0. If the product of two numbers is 0, then at least one of the factors must be 0. For any two numbers x and y, exactly one of the following is true: (1) x 5 y; x is equal to (the same as) y (2) x. y; x is greater than (bigger than) y (3) x, y; x is less than (smaller than) y. This is sometimes known as the trichotomy property. If ax 2 1 bx 1 c 5 0 and a 0, then x 5 2b 6 "b2 2 4ac 2a The radicand b 2 2 4ac is called the discriminant of the quadratic. A statement of order. The comparison property tells us that if two quantities are not exactly equal, we can relate them with a greater-than or a less-than symbol (called an inequality symbol). Both sides of an inequality may be multiplied or divided by a positive number, and the order of the inequality will remain unchanged. The order is reversed if both sides are multiplied or divided by a negative number. That is, if a, b then ac, bc if c. 0 and ac. bc if c, 0. This also applies to,., and. The solution of an inequality is unchanged if you add the same number to both sides of the inequality. If two quantities are equal, one may be substituted for the other without changing the truth or falsity of the statement. To find the values of the variable that make the inequality true.

9 Sum Difference Product Quotient Consecutive integers Translate Ratio Proportion Solving the proportion Percent

10 The result from subtraction. The result of an addition. The result of a division. The result of a multiplication. The process of writing an English sentence in mathematical symbols. Integers that differ by 1. A statement of equality between two ratios. For example, a b 5 c d For this proportion, a and d are called the extremes; b and c are called the means. The quotient of two numbers or expressions. The ratio of a given number to 100. This means that a percent is the numerator of a fraction whose denominator is 100. Finding the missing term of a proportion.

11 Percentage The percent problem Rate Base

12 A is P% of W is formulated as a proportion P A W The given amount in a percent problem. In a percent problem, it is the whole quantity. In percent problems, it is the percent.

Algebra I Unit Report Summary

Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02