9-2 Factoring Using The Distributive Property - Winston-Salem/Forsyth .
9 2 factoring using the distributive property Warm up: p. 479 #72 86 even Title: Factoring Using the Distributive Property February 19, 2013 Factoring by using the distributive property You can reverse what we learned in chapter 8 to express a polynomial as the product of a monomial factor and a polynomial factor. Example: Factored form: EQ: How do we factor polynomials by using the distributive property? How do we solve quadratic equations of the form ax bx c? Feb 19 11:53 AM Feb 19 11:53 AM Notes cont. Factoring involves finding the GCF Example: Now you write each term as the product of the GCF (divide it out) Example: This will give you the factored form of: Use the Distributive Property to factor . First, find the CGF of 15x and . Factor each number. Circle the common prime factors. GFC: Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF. Rewrite each term using the GCF. Simplify remaining factors. Distributive Property Feb 19 11:53 AM Feb 19 11:53 AM 1
9 2 factoring using the distributive property February 19, 2013 Use the Distributive Property to factor . Factor each number. Circle the common prime factors. GFC: or Rewrite each term using the GCF. Distributive Property The Answer: factored form of is Feb 19 11:53 AM Feb 19 11:53 AM Use the Distributive Property to factor each polynomial. a. Answer : b. Answer : Example 2 1b Feb 19 11:53 AM Feb 19 11:58 AM 2
9 2 factoring using the distributive property February 19, 2013 Grouping to factor If a polynomial has four or more terms it helps to group the polynomial and then factor. This means you take and split the polynomial into pairs. HINTS for grouping: There are four or more terms Terms with common factors should be grouped together. The two common factors are identical or additive inverses of each other. Example: Factor Answer : Feb 19 11:53 AM Feb 19 11:53 AM The additive inverse property Recognizing the polynomial as additive inverses can be VERY helpful when factoring by grouping. Additive inverses are like (x 7) (7 x). You know they are additive inverses bc when you add them together the sum is 0. Parenthesis are identical except for signs! You need to pull out a negative in one of the outside numbers Example: Factor Group terms with common factors. Parenthesis are identical except for signs! You need to pull out a negative in one of the outside numbers 3a ﴾ 5 b﴿ 4 ﴾b is outside goes in one parenthesis and – 5﴿What what is inside goes onto another. Answer : Distributive Property Example 2 3a Feb 19 11:53 AM Feb 19 11:53 AM 3
9 2 factoring using the distributive property February 19, 2013 Factor Factor Answer : Answer : Distributive Property Example 2 3b Feb 19 11:53 AM Zero product property If the product of two factors is 0, then at least one of the two factors is 0. Feb 19 11:53 AM Feb 19 11:53 AM Solve an equation in factored form Set up the two binomials so they are equal to zero and then solve for the variable. Example: Feb 19 11:53 AM 4
9 2 factoring using the distributive property Solve If either Check Substitute 2 and for x in the original equation. Then check the solutions. , then according to the Zero Product Property or Original equation or February 19, 2013 Set each factor equal to zero. Solve each equation. Answer: The solution set is Example 2 4a Feb 19 11:53 AM Example 2 4a Feb 19 11:53 AM Solve and equation by factoring Solve Then check the solutions. Write the equation so it is in the form of ab 0 Then solve for x. Example: Answer: {3, –2} Example 2 4b Feb 19 11:53 AM Feb 19 11:53 AM 5
9 2 factoring using the distributive property Answer: The solution set is Check by substituting 0 and for y in the original equation. Solve Then check the solutions. Write the equation so that it is of the form Original equation Subtract or February 19, 2013 from each side. Factor the GCF of 4 y and Zero Product Property which is 4y. Solve each equation. Example 2 5a Feb 19 11:53 AM Example 2 5a Feb 19 11:53 AM Practice/HW Solve P. 484 #32 62 even Answe r: Example 2 5b Feb 19 11:53 AM Feb 19 11:53 AM 6
9 2 factoring using the distributive property 2 February 19, 2013 Feb 19 11:53 AM Feb 19 11:53 AM Factor each number. Circle the common prime factors. Use the Distributive Property to factor. Rewrite each term using the GCF. Distributive Property Answer: The factored form of is GFC: or Feb 19 11:53 AM Example 2 1b
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Factoring . Factoring. Factoring is the reverse process of multiplication. Factoring polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers. For example, 2 3. 6 Similarly, any
241 Algebraic equations can be used to solve a large variety of problems involving geometric relationships. 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring Trinomials of the Form x2 bx c 5.4 Factoring Trinomials of the Form ax2 bx c 5.5 Factoring, Solving Equations, and Problem Solving
Factoring Polynomials Martin-Gay, Developmental Mathematics 2 13.1 – The Greatest Common Factor 13.2 – Factoring Trinomials of the Form x2 bx c 13.3 – Factoring Trinomials of the Form ax 2 bx c 13.4 – Factoring Trinomials of the Form x2 bx c by Grouping 13.5 – Factoring Perfect Square Trinomials and Difference of Two Squares
