QUADRATICS WKST QUADRATICS WKST QUADRATICS WKST WORKSHEET KEY

QUADRATICS WKST

QUADRATICS WKST

QUADRATICS WKST

WORKSHEET KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

FACTORING WHEN A = 1 SECTION 4. 3 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 5

STEPS IN FACTORING POLYNOMIALS A. Determine if there is a GCF. If there is, take it out. B. Make sure the equation equals to zero. 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 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 6

Factor f(x) = x 2 – 5 x + 6 SUM 12/5/2020 6: 36 PM PRODUCT EXAMPLE 1 4. 3: Factoring and Solving when a = 1 TS TP – 5 +6 7

EXAMPLE 1 Factor f(x) = x 2 – 5 x + 6 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 TS TP – 5 +6 8

EXAMPLE 2 Factor 27 = x 2 + 6 x 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 9

EXAMPLE 3 Factor f(x) = 4 x 2 – 4 x – 48 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 10

YOUR TURN Factor f(x) = x 3 – x 2 – 42 x 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 11

EXAMPLE 4 Factor f(x) = x 2 – 64 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 12

EXAMPLE 5 Solve x 2 + 64 = 0 Prime 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 13

SOLVING BINOMIALS A. Make sure the equation EQUALS TO ZERO (x 2 should always POSITIVE) B. Determine if there is a GCF C. Determine the Target Product and Target Sum of the equation 1. Multiply the First and Last Term 2. Ensure the terms adds to the middle and multiplies the end 3. Rewrite the problem with the new middle terms 4. 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 F. Put each equation to zero and solve G. If there any answers that repeat, they are known as multiple roots. (i. e. Double Root, Triple Root, etc…) 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 14

EXAMPLE 6 Solve x 2 – 64 = 0 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 15

EXAMPLE 7 Solve 4 x 2 – 4 x – 48 = 0 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 16

EXAMPLE 8 Solve 2 x 3 + 16 x 2 = 130 x 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 17

YOUR TURN Solve 3 x 3 + 3 x 2 – 126 x = 0 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 18

EXAMPLE 9 Solve 14 x – 49 = x 2 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 19

YOUR TURN Solve 2 x 2 + 20 x + 50 = 0 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 20

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 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 21

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 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 22

EXAMPLE 11 A rectangular picnic site measures 24 feet by 10 feet. You want to double the site’s area by adding the same distance x to the length and width. What are the dimensions? 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 23

YOUR TURN You have a rectangular garden in your background that measures 15 ft. by 10 ft. You want to double the area of the garden by adding the same distance x to the length and width. Find the new dimensions of the garden. 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 24

ASSIGNMENT Pg 256 3 -23 EOO, 25 -43 odd, 57, 61 12/5/2020 6: 36 PM 4. 3: Factoring and Solving when a = 1 25