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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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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

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

(-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

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?

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 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!