Solving problems by factoring
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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 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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If a number is added to its square the result is 56 what is the number
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 number1
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 901
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 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 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 what are the numbers
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 what are the numbers1
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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