1. Solving Problems by Factoring

2. 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

3. 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 = n – 7 = 0
n = n = 7
Check the answers
(-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 = n – 9 = 0
n = n = 9
The 2 negative integers are
-10 and -9

6. 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

7. 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 = w = 7

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

10. Tonight’s homework