Solving Equations Examples And Worksheet Page 8
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14A56
Appendix A
Review of Fundamental Concepts of Algebra
Polynomial Equations of Higher Degree
The methods used to solve quadratic equations can sometimes be extended to solve
WARNING / CAUTION
polynomial equations of higher degree.
A common mistake that is made
Example 10
Solving a Polynomial Equation by Factoring
in solving equations such as the
equation in Example 10 is to
4
2
divide each side of the equation
Solve
3x
48x
.
2
by the variable factor
x
.
This
Solution
loses the solution
x
0.
When
solving an equation, always
First write the polynomial equation in general form with zero on one side, factor the
write the equation in general
other side, and then set each factor equal to zero and solve.
form, then factor the equation
4
2
3x
48x
Write original equation.
and set each factor equal to
4
2
zero. Do not divide each side of
3x
48x
0
Write in general form.
an equation by a variable factor
2
2
3x
x
16
0
Factor out common factor.
in an attempt to simplify the
equation.
2
3x
x
4 x
4
0
Write in factored form.
2
3x
0
x
0
Set 1st factor equal to 0.
x
4
0
x
4
Set 2nd factor equal to 0.
x
4
0
x
4
Set 3rd factor equal to 0.
You can check these solutions by substituting in the original equation, as follows.
Check
✓
4
2
3
0
48
0
0 checks.
✓
4
2
3
4
48
4
4
checks.
✓
4
2
3
4
48
4
4 checks.
So, you can conclude that the solutions are
x
0,
x
4,
and
x
4.
Now try Exercise 113.
Example 11
Solving a Polynomial Equation by Factoring
3
2
Solve
x
3x
3x
9
0.
Solution
3
2
x
3x
3x
9
0
Write original equation.
2
x
x
3
3 x
3
0
Factor by grouping.
2
x
3 x
3
0
Distributive Property
x
3
0
x
3
Set 1st factor equal to 0.
±
2
x
3
0
x
3
Set 2nd factor equal to 0.
The solutions are
x
3,
x
3,
and
x
3.
Check these in the original
equation.
Now try Exercise 119.
ADVERTISEMENT
0 votes
Related Articles
Related forms
2.4 Write Equations Of Lines Examples And Worksheet - Chapter 2, Linear Equations And Functions
Education
Chapter 5 Solving Systems Of Linear Equations - 5.5 Solving Equations By Graphing Worksheet
Education
Lesson 3.3, 3.4, And 3.5: Adding, Subtracting, And Multiplying Integers Examples And Worksheets
Education
Capacity And Weight In The Customary System Examples And Worksheet - Chapter 8 Systems Of Measurement
Education
Related Categories
Parent category: Education