ENHANCED MATH 8

• To find the greatest common factor (GCF) of monomials, we can use listing or prime factorization
• Factoring polynomials completely


  1. Find common monomial factor

  2. Use distributive property
• Monomial


  A polynomial with only one term
• Standard form


  Polynomial arranged in descending order of degree
• Greatest common factor (GCF)

  The common factor having the greatest numerical factor and variables with the least degree
• Finding GCF by listing

  1. List factors of each monomial

  2. Find the common factors

  3. The GCF is the factor with the greatest numerical value and lowest variable degree
• Finding GCF by prime factorization

  1. Find the prime factors of each monomial

  2. The GCF is the product of the common prime factors with the lowest variable degree
• Factoring polynomials


  1. Find the GCF

  2. Factor out the GCF

  3. Factor the remaining polynomial using distributive property
• Factoring polynomials means rewriting them as a product of smaller degree polynomials
• Using the distributive property is another way to factor polynomials
• Rearranging the given polynomial can help find the GCF when it is not obvious
• Factoring the greatest common monomial factor
• Factoring polynomials


  • It is the reverse of multiplying a monomial and polynomial
  • Examples are provided of factoring polynomials by identifying the GCF and rewriting the polynomial as a product of the GCF and other factors
  • The process of factoring out the GCF is demonstrated step-by-step for several examples
• nts will complete an activity identifying common factors in pictures and practice problems are assigned to reinforce the skill
• Factoring the Difference of Two Squares

  Using the identity x^2 - y^2 = (x + y)(x - y)
• Algebraic expressions involving variables


  • x, y, a, b, c, d, e, m, n, p, q
• The worksheet includes the student's name, grade/section, date, and score at the top for identification and grading purposes
• Factoring polynomials by common monomial factor

  Finding the greatest common monomial factor (GCM), which is the greatest common factor of the coefficients multiplied by the greatest common factor of the variables
• Expressions to factor


  • 3x + 3y
  • 2x^3 - 6x^2
• Factoring is finding the factors and the GCM is the product of the coefficient and variable GCFs
• Linear equation


  Can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero
• The document discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation
• Factoring polynomials


  Finding the greatest common factor (GCF), factoring trinomials of the form x^2 + bx + c, and factoring trinomials of the form ax^2 + bx + c
• The document provides instructions and examples on the various methods of factoring polynomials
• Zero exponents, negative integral exponents, rational exponents, and radicals

  Covered in Grade 9 Mathematics Unit 4
• Linear inequalities in two variables

  Introducing linear inequalities and their notation, determining if an ordered pair is a solution, and graphing linear inequalities
• Factoring


  The financial transaction where a business sells its accounts receivable to a third party called a factor
• Factoring provides firms with working capital and credit protection, and involves three main parties - the client firm, its customers, and the financial institution factor
• Quadratic equation


  An equation of degree 2 that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0
• Solving quadratic equations by factoring


  Identifying quadratic equations, rewriting them in standard form, and factoring trinomials of the form x^2 + bx + c
• Rational algebraic expressions


  Simplifying and illustrating rational algebraic expressions
• Rational expressions


  Solving rational equations by finding the LCD and canceling common factors
• Factoring the sum and difference of two cubes

  Using steps like identifying common factors, taking cube roots, and forming trinomial expressions
• Multiplying polynomials


  Using the distributive property, horizontal and vertical methods, and techniques like FOIL and grouping
• Squaring a binomial


  Results in a trinomial with the square of the first term, twice the product of the terms, and the square of the last term
• Factoring polynomials by finding the greatest common factor (GCF)


  The GCF is a number, variable, or combination that is common to each term
• Steps for factoring polynomials with common monomial factors

  Find the GCF, divide the polynomial by the GCF, express the polynomial as a product of the quotient and the GCF
• Factoring


  The reverse of multiplication and finding the prime factors of an expression
• Greatest common monomial factor (GCM)

  • The greatest common factor of the coefficients multiplied by the greatest common factor of the variables
• Expressions to factor


  • 3x + 3y
  • 2x^3 - 6x^2