 • Slides: 24    Worksheet Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. EXAMPLE 10 A town has a nature preserve with a rectangular field that measures 600 meters by 400 meters. The town wants to double the area of the field by adding land as shown. What are the dimensions of the field? x 400 m 600 m x 10/23/2021 5: 01 AM 4. 3: Factoring and Solving when a = 1 5 EXAMPLE 10 A town has a nature preserve with a rectangular field that measures 600 meters by 400 meters. The town wants to double the area of the field by adding land as shown. What are the dimensions of the field? x 400 m 600 m x 10/23/2021 5: 01 AM 4. 3: Factoring and Solving when a = 1 6 Solving Quadratic Equations when a > 1 and by factoring with GCF Section 4. 4 10/23/2021 5: 01 AM 5. 3 - Solving Quadratic Equations by Factoring 7 Factoring Steps when a>1 A. Make sure the equation is all on ONE side B. Determine if there is a GCF C. Determine the Target Product and Target Sum of the equation 1. 2. 3. 4. Multiply the First and Last Term Ensure the terms adds to the middle and multiplies the end Rewrite the problem with the new middle terms Make sure that one of the binomials is the same on both sides D. Factor by Grouping by Splitting the Terms E. Combine like terms and multiply Factor 2 x 2 + 5 x + 2 SUM PRODUCT Example 1 What number adds up to +5 and multiplies to +4 Example 1 Factor 2 x 2 + 5 x + 2 You must add an X to the middle term because it has to match the original equation This sign should ALWAYS be bought down Example 2 Factor 3 x 2 + 20 x – 7 Example 3 Factor 2 x 2 – 9 – 3 x Your Turn Factor 4 x 2 + 4 x – 3 Example 4 Solve 3 x 2 + 10 x – 8 = 0 Don’t forget the xy in the middle Example 5 Solve 5 x 2 – 27 x = 18 Your Turn Solve 4 x 2 – 10 x + 15 = 10 x – 10 Example 6 Solve 16 x 2 – 1 = 0 Don’t forget the xy in the middle Example 7 Solve 9 x 2 – 64 = 0 Your Turn Solve 36 x 2 – 9 = 0 Example 8 Factor 8 x 2 – 14 xy + 3 y 2 Don’t forget the xy in the middle Your Turn Factor 6 xy 2 + 33 xy – 18 x… Example 9 You have made a rectangular quilt that is 5 feet by 4 feet. You want to use the remaining 10 square feet of fabric to add border of uniform width to the quilt. What should the width of the quilt’s border be? Example 9 You have made a rectangular quilt that is 5 feet by 4 feet. You want to use the remaining 10 square feet of fabric to add border of uniform width to the quilt. What should the width of the quilt’s border be? Assignment Page 263 3 -19 EOO, 23 -29 odd, 33 -57 EOO