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Solving Problems by Factoring

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 form. Check the answers. If a number is added to its square, the result is 56. What is the number?. Let n = number n + n 2 = 56

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Solving Problems by Factoring

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  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 + n2 = 56 • Put in standard form • n2 + n – 56 = 0 • (n+ 8) ( n – 7) = 0 • n + 8 = 0 n – 7 = 0 • n = -8 n = 7 Check the answers (-8)2 + -8 = 56 (7)2 + 7 = 56

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

  5. Find two consecutive negative integers whose product is 90 • n = 1st integer • n + 1 = 2nd integer • (n) (n+1) = 90 • n2 + n = 90 • n2 + 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 cm2. What are the dimensions of the rectangle? L x W = A Label

  7. The length of a rectangle is 8 cm. greater than its width. The area is 105 cm2. What are the dimensions of the rectangle? w L x W = A w (w + 8 ) = 105 w+8 w2 + 8 w = 105 The width is 7 The length is 15 w2 + 8w – 105 = 0 (w+15)(w-7) = 0 w = -15 w = 7

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

  9. The sum of 2 numbers is 25. The sum of their squares is 313. What are the numbers? • n = 1st number • 25 – n = 2nd number • (n)2 + (25-n)2 = 313 • n2 + 625 –50n + n2 = 313 • 2n2 –50n + 625 = 313 • 2n2 – 50 n +312 = 0 • Divide by 2 • n2 – 25n + 156 = 0 • (n – 12 )(n – 13) = 0 • n = 12 n = 13 Check the numbers 12 2 + 13 2 = 313 ?? 144 + 169 = 313 ?? Yuppp!

  10. Tonight’s homework

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