Section 6.4 Factoring Special Forms

6.4 Lecture Guide: Factoring Special Forms Objective 1: Factor perfect square trinomials.

Algebraically Square of a Sum Square of a Difference Verbally A trinomial that is the square of a binomial has: 1. a first term that is a ____________ of the first term of the binomial. 2. a middle term that is ____________ the product of the two terms of the binomial. 3. a last term that is a ____________ of the last term of the binomial. Algebraic Example

Complete the following table. ProductsFactors

Determine the missing terms so each given trinomial is a perfect square trinomial

Determine the missing terms so each given trinomial is a perfect square trinomial

Objective 2: Factor the difference of two squares. AlgebraicallyVerbally The difference of the squares of two terms factors as the ____________ of these terms times their ___________. Algebraic Example Difference of Two Squares

Factor each difference of two squares. ProductsFactors

Algebraically is Verbally The ____________ of two squares is prime. Algebraic Example is prime. A common error is to factor an expression like as Sum of Two Squares prime* * For binomials of degree greater than two this statement is not always true. Second degree polynomials that are the sum of two squares do not factor!

Factor each binomial if possible

Factor each binomial if possible

Objective 3: Factor the sum or difference of two cubes. Find each product. 27.

Find each product. 28.

29. Which of the above is the correct factorization of ?

Sum or Difference of Two Cubes Algebraically Verbally Write the binomial factor as the sum (or difference) of the two cube roots. Then use the binomial factor to obtain each term of the trinomial : Algebraic Example

Sum or Difference of Two Cubes – Cont. Algebraically Verbally 1. The _________ of the first term of the binomial is the first term of the trinomial factor. 2.The opposite of the ___________ of the two terms of the binomial is the second term of the trinomial factor. 3.The _________ of the last term of the binomial is the third term of the trinomial factor. Algebraic Example

Factor each sum or difference of two cubes. ProductsFactors

Factor each polynomial if possible. Don’t forget to check for a GCF first. 37.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 38.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 39.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 40.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 41.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 42.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 43.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 44.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 45.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 46.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 47.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 48.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 49.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 50.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 51.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 52.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 53.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 54.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 55.

Factor each polynomial if possible. Don’t forget to check for a GCF first. 56.