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8-3A Factoring Quadratic Trinomials There are numerous methods to factor trinomials. The method used in this presentation is NOT in your textbook. Please pay attention as this method is easier to use than the method presented in the book! Algebra 1 Glencoe McGraw-Hill Linda Stamper In the previous lesson, you solved a quadratic equation by factoring. The problem. Set each factor equal to zero and solve! x 3x 5 0 x 3 0 x 3 or x5 0 or x 5 The factors were given information. Today you will need to find the factors of a quadratic trinomial. x+2 Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle. x2 5x 6 x 3 x 3x 2 You need to find the factors! You are given the product – quadratic trinomial! x+3 Because multiplication is commutative, it will not matter what order you write the factors. x2 5x 6 x 2 x 2x 3 You to The need factors findchanged the have factors! order! This is the same quadratic trinomial Algebra tiles are not very practical for finding factors of a quadratic trinomial. Using what you know about product and sum puzzles will help you to factor trinomials when the leading coefficient is 1. x2 6x 7 ax2 bx c leading coefficient standard form for a quadratic trinomial Factor. Multiply a times c to find the product. ax2 bx c 15 x2 8x 8 15 5 3 Draw an X on your x x b in the bottom represents the sum paper. To fill in the sides of the x you must find two This quadratic numbers that have a product of trinomial 15 and a sum of 8. is an expression. Place the values from the sides of theHow X figure into do you know it is NOT your factors. an equation? Check by doing You know FOIL in your there will be head! an x in each factor! All of today’s problems involving quadratic trinomials will have a leading coefficient of 1. Multiply a times c to find the product. –3 ax2 bx c x2 –22x 3 –33 1 x x b in the bottom represents the sum To fill in the sides of the x you must find two numbers that have a product of –3 and a sum of –2. Place the values from the sides of the X figure into your factors. Check by doing You know FOIL in your there will head! be an x in each factor! Example 1 Factor. 1. Write the problem. 2. Draw an X next to the problem. ax2 bx c x2 7x 12 x x 12 +4 4 +3 3 7 3. Multiply a times c to find the product. 4. Write b in the bottom to represent the sum. 5. Fill in the sides of the x by finding two numbers that have a product of the top Check by number and a sum of the bottom number. doing FOIL 6. Using the values from the sides of in your the X figure write the factors. Your head! factors must be in parentheses! Factor. Example 2 Example 3 x 9x 20 x2 8x 9 Example 4 Example 5 2 x2 3x 18 x2 6x 7 Factor. Example 3 Example 2 x2 9x 20 x 5x 4 20 –5 –4 –9 x2 8x 9 –9 x 9x 1 –9 1 –8 Check by doing FOIL in your head! Your binomial factors must be in parentheses! Factor. Example 4 Example 5 –18 x2 3x 18 x 6x 3 6 –3 3 x2 6x 7 x 7 x 1 Check by doing FOIL in your head! –7 7 –1 6 Factor. 1) x2 4x 3 x 1x 3 2) x2 5x 4 x 1x 4 6) x2 4x 4 x 2x 2 7 ) x2 3x 10 x 5x 2 3) x2 5x 6 x 6x 1 8) x2 2x 8 x 4 x 2 4) x2 x 6 x 3x 2 9) x2 8x 7 x 1x 7 5) x2 5x 6 x 2x 3 10) x2 8x 7 x 7 x 1 8-A5 Handout A5 and Page 439 # 49, 51- 53, 58-63.