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Solving Problems by Factoring. If a number is added to its square, the result is 56. What is the number?  Let n = number  Set up:  Put in standard.

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Presentation on theme: "Solving Problems by Factoring. If a number is added to its square, the result is 56. What is the number?  Let n = number  Set up:  Put in standard."— Presentation transcript:

1 Solving Problems by Factoring

2 If a number is added to its square, the result is 56. What is the number?  Let n = number  Set up:  Put in standard form Check the answers

3 If a number is added to its square, the result is 56. What is the number?  Let n = number  n + n 2 = 56  Put in standard form  n 2 + n – 56 = 0  (n + 8) ( n – 7) = 0  n + 8 = 0 n – 7 = 0  n = -8 n = 7 Check the answers (-8) = 56 (7) = 56

4 Find two consecutive negative integers whose product is 90  1 st integer =  2 nd integer =  Set up:

5 Find two consecutive negative integers whose product is 90  n = 1 st integer  n + 1 = 2 nd integer  (n) (n+1) = 90  n 2 + n = 90  n 2 + n – 90 = 0  (n +10) ( n – 9 ) = 0  n + 10 = 0 n – 9 = 0  n = -10 n = 9 The 2 negative integers are -10 and-9

6 The length of a rectangle is 8 cm. greater than its width. The area is 105 cm 2. What are the dimensions of the rectangle? Label L x W = A

7 The length of a rectangle is 8 cm. greater than its width. The area is 105 cm 2. What are the dimensions of the rectangle? w w+8 L x W = A w (w + 8 ) = 105 w w = 105 w 2 + 8w – 105 = 0 (w+15)(w-7) = 0 w = -15 w = 7 The width is 7The length is 15

8 The sum of 2 numbers is 25. The sum of their squares is 313. What are the numbers?  1 st number =  2 nd number =  Set up: Check the numbers

9 The sum of 2 numbers is 25. The sum of their squares is 313. What are the numbers?  n = 1 st number  25 – n = 2 nd number  (n) 2 + (25-n) 2 = 313  n –50n + n 2 = 313  2n 2 –50n = 313  2n 2 – 50 n +312 = 0  Divide by 2  n 2 – 25n = 0  (n – 12 )(n – 13) = 0  n = 12 n = = 313 ?? = 313 ?? Yuppp! Check the numbers

10 Tonight’s homework


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