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Solving Problems by Factoring

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Solving Problems by Factoring

- Let n = number
- Set up:
- Put in standard form

Check the answers

- 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

- 1st integer =
- 2nd integer =
- Set up:

- 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

L x W = A

Label

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

Check the numbers

- 1st number =
- 2nd number =
- Set up:

- 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!