Solving a Quadratic Equation with a Common FactorSolve
Standard form
Factor out 2.
Divide each side by 2.
Factor.
Zero-factor property
Solve each equation.Checkeach solution to verify that the solution set is E. NOW TRY
52 , 4F
p=
5
2
2 p= 5 p= 4
2 p- 5 = 0or p- 4 = 0
12 p- 521 p- 42 = 0
2 p^2 - 13 p+ 20 = 0
212 p^2 - 13 p+ 202 = 0
4 p^2 - 26 p+ 40 = 0
4 p^2 + 40 = 26 p
4 p^2 + 40 = 26 p.
EXAMPLE 3
CHECK Let Let
✓ True ✓ True
Both solutions check, so the solution set is
(b)
Subtract yand 20.
Factor.
Zero-factor property
Solve each equation.Checkeach solution to verify that the solution set is 5 - 4, 5 6. NOW TRY
y= 5 or y=- 4
y- 5 =0or y+ 4 = 0
1 y- 521 y+ 42 = 0
y^2 - y- 20 = 0
y^2 =y+ 20
5 2, 3 6.
- 6 =- 6 - 6 =- 6
4 - 10 - 6 9 - 15 - 6
22 - 5122 - 6 3 2 - 5132 - 6
x^2 - 5 x=- 6 x 2 - 5 x=- 6
x= 2. x= 3.
394 CHAPTER 6 Factoring and Applications
NOW TRY
EXERCISE 2
Solve .t^2 =- 3 t+ 18
NOW TRY
EXERCISE 3
Solve. 10 p^2 + 65 p= 35
Write this equation
in standard form.
Standard formSolving a Quadratic Equation by Factoring
Step 1 Write the equation in standard form— that is, with all terms on
one side of the equals symbol in descending powers of the variable
and 0 on the other side.
Step 2 Factorcompletely.
Step 3 Use the zero-factor propertyto set each factor with a variable
equal to 0.
Step 4 Solvethe resulting equations.
Step 5 Checkeach solution in the original equation.This 2 is not
a solution of
the equation.NOW TRY ANSWERS
- 5 - 6, 3 6 3.E-7,^12 F
NOTE Not all quadratic equations can be solved by factoring. A more general
method for solving such equations is given in Chapter 9.
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