Material of support

Content: Basic algebra

Cases of factoring

Objectiv: Demonstrate the ability to pose and solve problems using the properties of algebraic operations Identify the different methods of factorization and its application in everyday contexts

ALGEBRA Algebra is a branch of mathematics that studies the numbers and their properties in general. You do not need the value of a number to know their properties and operate, for it substitutes a symbol usually a letter. By starting with the study of algebra appear new expressions, which we call algebraic expressions, and to identify appropriate name them properly during any exchange of information. Thus, the set of numbers and letters that represent transactions between quantities is called algebraic expression. These are composed of terms:

Algebraic term: An algebraic term is the product of one or more variables and a literal or numeric constant.

- 3x2y

Degree of a term: It is called an algebraic degree of the sum of the exponents of its literal term factor. But you can also define the degree of a term by the exponent of the literal parts, eg:

-3x2y

Grade regarding X is 2 and the degree to Y is 1

EXERCISE: For each of the following algebraic terms, determines its sign, numerical coefficient, and degree literal factor,

compare your results to the table:

Exercise Sign Coefficent Literal part Grade

– 5,9a2b3c negative 5,9 a2b3c 2+3+1=6

54

3

3kh

negative

3

3

h4k5 4 + 5 = 9

abc positiv 1 abc 1 +1 +1 = 3

4

2xy

positiv 1/4 xy2 1 + 2= 3

– 8a4c2d3 negative 8 a4c2d3 4 + 2 + 3 =9

Sign coefficient

Literal part

Exponent

Algebraic expressions: algebraic expression is the result of combining, through the operation of addition, one or

more algebraic terms.

Example:

Number of terms: Depending on the number of terms that possesses an algebraic expression is called:

Monomial: An algebraic term : a2bc4 ; –35z

Binomial: Two algebraic terms : x + y ; 3 – 5b

Trinomio: Three algebraic terms : a + 5b -19

Polynomial: Over two algebraic terms : 2x – 4y + 6z – 8x2

Degree of a polynomial: The degree of a polynomial is determined by the highest degree of any term whose

coefficient is nonzero.

Exercise:

Determines the degree and classified according to the number of terms, the following algebraic expressions,

compare your results with the table:

Algebraic expression Expression level Number of terms

2x – 5y3 1; 3 = 3 2: binomio

4

32yx

2; 3 = 3 1: Monomio

a – b + c – 2d 1; 1; 1; 1; 1 = 1 4: Polinomio

m2 + mn + n2 2; 2; 2 = 2 3: Trinomio

x + y2 + z3 – xy2z3 1; 2; 3; 6 = 6 4: Polinomio