Solving Problems by Factoring

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Presentation transcript:

Solving Problems by Factoring

If a number is added to its square, the result is 56 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 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

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

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

The length of a rectangle is 8 cm. greater than its width 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

The length of a rectangle is 8 cm. greater than its width 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

The sum of 2 numbers is 25. The sum of their squares is 313 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:

The sum of 2 numbers is 25. The sum of their squares is 313 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!

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