math

• Factoring polynomials


  Using the same concept of factoring integers - looking for simpler monomials or binomials whose product is equal to the binomial/trinomial being factored
• Techniques used in factoring polynomials


  • Looking for common factors
  • Using special factoring patterns
• Factor


  A number or term that is multiplied by another factor
• Factoring


  Finding all the factors for a number or polynomial
• Common factor


  A factor that appears in all terms of the polynomial, can be a number, variable, or combination
• Quadratic polynomial


  A polynomial of the 2nd degree
• Factoring quadratic polynomials


  1. Find the values of m and n so that (x+m)(x+n) = ax^2 + bx + c

  2. When a=1, b>0, c>0 then m and n are positive

  3. When a=1, b<0, c>0 then one of m or n is negative

  4. When a=1, c<0 then factor out the negative first
• To factor a polynomial completely:
• Factoring binomials


  1. Look for the greatest common factor (can be a number or variable) in both terms

  2. Divide both terms by the common factor

  3. Put parentheses around the terms divided by the common factor

  4. Put the common factor outside the parentheses
• Difference of two squares


  a^2 - b^2 = (a + b)(a - b)
• Square of a binomial


  a^2 + 2ab + b^2 = (a + b)^2

  a^2 - 2ab + b^2 = (a - b)^2
• Factoring by groups


  If 4 or more terms, factor common monomials from groups of terms, then see if there is a common binomial factor
• Solving quadratic expressions ax^2 + bx + c where a ≠ 1


  Find the product ac

  Look for two numbers that multiply to ac and add up to b

  Rewrite the bx term into two terms using the numbers found

  Factor the expression by grouping
• Zero-product property


  If two numbers multiply to zero, then at least one of those numbers must be zero
• Solving polynomial equations by factoring


  Rewrite the equation in standard form so right side equals zero

  Factor the polynomial completely

  Use the zero-product property to set each factor equal to zero

  Solve each equation