The middle term of the trinomial is x so we look for the sum of the integers

The middle term of the trinomial is x so we look for

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The middle term of the trinomial is x , so we look for the sum of the integers that equals 1. Since no sum exists for the given combinations, we say that this polynomial is prime (irreducible) over the integers. Determine the sum of the integers. Integers whose product is 8 1, 8 1, 8 4, 2 4, 2 Integers whose product is 8 1, 8 1, 8 4, 2 4, 2 Sum 7 7 2 2 Study Tip In Example 9, Step 3, we can eliminate any factors that have a common factor since there is no common factor to the terms in the trinomial.
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0.4 Factoring Polynomials 45 1. Factor out the greatest common factor (monomial). 2.Identify any special polynomial forms and apply factoring formulas. 3. Factor a trinomial into a product of two binomials: ( ax b )( cx d ). 4. Factor by grouping. S TRATEGY FOR FACTORING POLYNOMIALS Study Tip When factoring, always start by factoring out the GCF. A Strategy for Factoring Polynomials The first step in factoring a polynomial is to look for the greatest common factor. When specifically factoring trinomials, look for special known forms: a perfect square or a difference of two squares. A general approach to factoring a trinomial uses the FOIL method in reverse. Finally, we look for factoring by grouping. The following strategy for factoring polynomials is based on the techniques discussed in this section. EXAMPLE 12 Factoring a Polynomial by Grouping Factor 2 x 2 2 x x 1. Solution: Group the terms that have a common factor. (2 x 2 2 x ) ( x 1) Factor out the common factor in each pair of parentheses. 2 x ( x 1) 1( x 1) Use the distributive property. (2 x 1)( x 1) YOUR TURN Factor x 3 x 2 3 x 3. EXAMPLE 13 Factoring Polynomials Factor: a. 3 x 2 6 x 3 b. 4 x 3 2 x 2 6 x c. 15 x 2 7 x 2 d. x 3 x 2 x 2 2 Solution (a): Factor out the greatest common factor. 3 x 2 6 x 3 3( x 2 2 x 1) The trinomial is a perfect square. 3( x 1) 2 Solution (b): Factor out the greatest common factor. 4 x 3 2 x 2 6 x 2 x (2 x 2 x 3) Use the FOIL method in reverse to factor the trinomial. 2 x (2 x 3)( x 1) Solution (c): There is no common factor. 15 x 2 7 x 2 Use the FOIL method in reverse to factor the trinomial. (3 x 2)(5 x 1) Solution (d): Factor by grouping. x 3 x 2 x 2 2 ( x 3 x ) (2 x 2 2) x ( x 2 1) 2( x 2 1) ( x 2)( x 2 1) Factor the difference of two squares. ( x 2)( x 1)( x 1) Answer: ( x 1)( x 2 3)
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46 CHAPTER 0 Prerequisites and Review Factoring a Trinomial as a Product of Two Binomials x 2 bx c ( x ?)( x ?) 1. Find all possible combinations of factors whose product is c . 2. Of the combinations in Step 1, look for the sum of factors that equals b . ax 2 bx c (? x ?)(? x ?) 1. Find all possible combinations of the first terms whose product is ax 2 . 2. Find all possible combinations of the last terms whose product is c .
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  • Summer '17
  • juan alberto
  • Fractions, Elementary arithmetic, Greatest common divisor

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