# Factoring to Solve Quadratic Equations - PowerPoint by wanghonghx

VIEWS: 48 PAGES: 6

• pg 1
```									          Factoring to Solve Quadratic
ALGEBRA 1 LESSON 10-5

(For help, go to Lessons 2-2 and 9-6.)

Solve and check eachEquations
equation.
1. 6 + 4n = 2             2. a – 9 = 4                 3. 7q + 16 = –3
8

Factor each expression.
4. 2c2 + 29c + 14         5. 3p2 + 32p + 20            6. 4x2 – 21x – 18

5-13
ALGEBRA 1 LESSON 10-5

Solutions       Equations
1. 6 + 4n = 2
4n = –4
n = –1
Check: 6 + 4(–1) = 6 + (–4) = 2
a
2. 8 – 9 = 4
a
8
= 13
a = 104
Check: 104 – 9 = 13 – 9 = 4
8
3. 7q + 16 = –3
7q = –19
q = –2 5
7
Check: 7 (–2 5 ) + 16 = 7(– 19 ) + 16 = –19 + 16 = –3
7               7

5-13
ALGEBRA 1 LESSON 10-5

Solutions (continued) Equations
4. 2c2 + 29c + 14 = (2c + 1)(c + 14)
Check: (2c + 1)(c + 14) = 2c2 + 28c + c + 14 = 2c2 + 29c + 14

5. 3p2 + 32p + 20 = (3p + 2)(p + 10)
Check: (3p + 2)(p + 10) = 3p2 + 30p + 2p + 20 = 3p2 + 32p + 20

6. 4x2 – 21x – 18 = (4x + 3)(x – 6)
Check: (4x + 3)(x – 6) = 4x2 – 24x + 3x – 18 = 4x2 – 21x – 18

5-13
ALGEBRA 1 LESSON 10-5

Equationsan open-top box. The total
The diagram shows a pattern for
area of the sheet of materials used to make the box is 130 in.2. The
height of the box is 1 in. Therefore, 1 in.  1 in. squares are cut from
each corner. Find the dimensions of the box.

Define: Let x = width of a side of the box.
Then the width of the material = x + 1 + 1 = x + 2
The length of the material = x + 3 + 1 + 1 = x + 5

Relate: length  width = area of the sheet

5-13
ALGEBRA 1 LESSON 10-5

Equations(continued)

Write: (x + 2) (x + 5) = 130

x2 + 7x + 10 = 130         Find the product (x + 2) (x + 5).

x2 + 7x – 120 = 0               Subtract 130 from each side.

(x – 8) (x + 15) = 0              Factor x2 + 7x – 120.

x–8=0             or     x + 15 = 0     Use the Zero-Product Property.

x=8                or     x = –15        Solve for x.

The only reasonable solution is 8. So the dimensions of the box are
8 in.  11 in.  1 in.

5-13
ALGEBRA 1 LESSON 10-5

Equations
1. Solve (2x – 3)(x + 2) = 0.
3
–2, 2
Solve by factoring.
2. 6 = a2 – 5a        3. 12x + 4 = –9x2   4. 4y2 = 25
2                   5
–1, 6             –                   ±
3                   2

5-13

```
To top