Factoring

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This presentation discusses the different methods to factor a quadratic equation.

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Factoring

  1. 1. FACTORING QUADRATICS
  2. 2. WHAT TO LOOK FOR Look for three terms. Look for only two terms. Look for only two terms. The coefficient of x is the sum of two numbers and the constant is the product of the same two numbers. The beginning & end terms are perfect squares and the middle term is doubled. Look for the variable to be cubed The first term must be squared. Look for two perfect squares being subtracted. Look for a coefficient in front of x. GENERIC RECTANGLE/ DIAMOND SHORT CUTS GCF
  3. 3. VOCABULARY <ul><li>Difference of squares - A special polynomial that can be factored as the product of the sum and difference of two terms. </li></ul><ul><li>Factor - Where two or more algebraic expressions are multiplied together, each of the expressions is a factor of the product. </li></ul><ul><li>Factored completely - A polynomial is factored completely if none of the resulting factors can be factored further. </li></ul><ul><li>Generic rectangle - An organizational device used for multiplying and factoring polynomials. </li></ul><ul><li>Greatest common factor - for a polynomial, the greatest common monomial factor of its terms. </li></ul><ul><li>Perfect square trinomials - Trinomials of the form are known as perfect square trinomials as </li></ul><ul><li>Polynomial - the sum or difference of two or more monomials. </li></ul><ul><li>Quadratic - A polynomial is quadratic if the largest exponent in the polynomial is two (that is, the polynomial has degree 2). </li></ul><ul><li>Term - Each part of the expression separated by addition or subtraction signs. </li></ul><ul><li>Variable - A variable is a symbol used in a mathematical sentence to represent a number. </li></ul>
  4. 4. GCF - TWO TERMS <ul><li>A big clue that you need to use the GCF is when there are only two terms </li></ul><ul><li>Examples </li></ul>
  5. 5. GCF - coefficient in front of x (a > 1) <ul><li>Another clue that you will need to use the GCF is when the coefficient in front of x is greater than 1. </li></ul><ul><li>Examples </li></ul>
  6. 6. GCF - X is cubed <ul><li>A third clue that you should use the GCF to factor is when the variable is cubed. </li></ul><ul><li>Examples </li></ul>
  7. 7. DIFFERENCE OF SQUARES (Short Cut) <ul><li>Here’s what to look for with difference of squares: </li></ul><ul><li>a. There are only two terms </li></ul><ul><li>b. Both terms are perfect squares. </li></ul><ul><li>c. The terms must be subtracted! </li></ul><ul><li>Once you determine an expression is a d i fference of </li></ul><ul><li>squares it’s very simple to factor. For example: </li></ul>
  8. 8. PERFECT SQUARE TRINOMIAL (Short cut) <ul><li>DESCRIPTION </li></ul><ul><li>If the first and third terms are squares, take their square </li></ul><ul><li>root, multiply them together and then multiply by 2. If </li></ul><ul><li>your solution is the quadratic's middle term, then you've </li></ul><ul><li>got a perfect square trinomial. </li></ul><ul><li>EXAMPLES </li></ul>
  9. 9. FACTORING COMPLETELY <ul><li>A polynomial is factored completely if none of the resulting factors can be factored further. </li></ul><ul><li>Examples This polynomial is factored completely: </li></ul>
  10. 10. GENERIC RECTANGLE & DIAMOND - SIMPLE <ul><li>After the GCF and the factoring short cuts, the next thing you should look for when factoring is to see if you can use the generic rectangle and diamond method. </li></ul><ul><li>Diamond Problems can be used to help factor easier quadratics like x 2 + 6x + 8. </li></ul>
  11. 11. GENERIC RECTANGLE & DIAMOND - COMPLEX <ul><li>We can modify the diamond method slightly to factor problems that are a little different in that they no longer have a “ 1 ” as the coefficient of x 2 . For example, factor: </li></ul>
  12. 12. REFERENCES <ul><li>Sallee, T., Kysh, J., Kasimatis, E.,(2002). CPM Algebra 1.Sacramento, CA </li></ul><ul><li>http://www.saab.org/mathdrills/factor.cgi - factoring practice </li></ul><ul><li>http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact1.htm - DOS </li></ul><ul><li>http://www.purplemath </li></ul><ul><li>http://www.mathvids.com/lesson/mathhelp/790-factoring-polynomials-using-gcf </li></ul><ul><li>http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_Factoring.xml </li></ul><ul><li>http://office.microsoft.com/en-us/clipart/download.aspx </li></ul>

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