CHECK
LetSimplify;✓ True
Check that 1 is a solution. The solution set is E-^72 , 1F. NOW TRY
15 = 15
1 - 6 2a-
5
2
b 9 + 6
1 - 7 + 1 2a- 1 = 22.
5
2
b 2 a
9
2
b + 6
c 2 a- x=- 27.
7
2
b + 1 da-
7
2
+ 1 b 2 c 1 - a-
7
2
bd+ 6
12 x+ 121 x+ 12 = 211 - x 2 + 6
SECTION 6.5 Solving Equations by Factoring 347
NOW TRY
EXERCISE 5
Solve.
= 41 x+ 42 - 41 x+ 3212 x- 12NOW TRY ANSWERS
- E-3, 25 F 6.E-4, 0, 23 F
The zero-factor property can be extended to solve certain polynomial equations
of degree 3 or greater, as shown in the next example.
Solving an Equation of Degree 3Solve
Add 6xto each side.
Multiply each side by
Factor out x.
Factor the trinomial.or or
x= 3 or x=- 2
x= 0 x- 3 = 0 x + 2 = 0
x 1 x- 321 x+ 22 = 0
x 1 x^2 - x- 62 = 0
x^3 - x^2 - 6 x= 0 - 1.
- x^3 + x^2 + 6 x= 0
- x^3 + x^2 =- 6 x
- x^3 +x^2 =- 6 x.
NOW TRY EXAMPLE 6
EXERCISE 6
Solve 12x= 2 x^3 + 5 x^2.
Extend the zero-factor property
to the three variablefactors.
Remember to set
xequal to 0.Check that the solution set is 5 - 2, 0, 3 6. NOW TRY
OBJECTIVE 2 Solve applied problems that require the zero-factor property.
An application may lead to a quadratic equation.
Using a Quadratic Equation in an ApplicationA piece of sheet metal is in the shape of a parallelogram. The longer sides of the par-
allelogram are each 8 m longer than the distance between them. The area of the piece
is Find the length of the longer sides and the distance between them.
Step 1 Readthe problem again. There will be two answers.
Step 2 Assign a variable.
Let the distance between the longer sides
and x+ 8 =the length of each longer side. (See FIGURE 1.)
x=
48 m^2.
EXAMPLE 7
x + 8x + 8xFIGURE 1