Name
Class
5-3
Date
Practice
Solving Polynomial Equations
Find the real or imaginary solutions of each equation by factoring.
3
1. x + 512 = 0
To start, write x3 + 512 as a sum
of cubes and factor.
x3 + 83 = 0
(x + 8)(x2 − 8x + 64) = 0
4
2
4
2
2
3. x + 5x = 6
4
3
2
5. 27x − 1 = 0
2. x − 3x = −2x
4. x + 2x = 10x
6. x + 4 = −4x
2
3
3
2
7. x + 10x + 24x = 0
Solve each equation.
8. x + 4x − 2x − 8 = 0
3
2
3
9. x – 6x + 5x = 0
5
3
10. x = 9x
11. 2x + 8x + 4x = −16
12. x − 25 = 0
13. 27x − 216 = 0
4
14. Writing Show how you can rewrite
Mrs. Steinberg – Algebra 2
3
2
3
x6 1

as a difference of two cubes.
y 9 27
Name
Class
Date
Practice (continued)
5-3
Solving Polynomial Equations
Find the real solutions of each equation using a graphing utility. Round to the nearest
hundredth.
15. x − 3x − 9x = −15
3
2
x3 − 3x2 − 9x + 15 = 0
To start, rewrite the equation with
one side equal to zero.
2
17. 2x − 2x + 4x = 3
4
16. 3x = 22x
18. −x + 1 = 2x
3
2
3
2
19. x − 2x − 5x + 1 = 0
4
3
2
For Exercises 20–22, write an equation to model each situation. Then solve each
equation by graphing. Use a graphing utility.
3
20. The volume V of a container is 61 in. . The width, the length, and the height are
x, x − 2, and x + 3 respectively. What are the container’s dimensions?
To start, write the equation of
x(x − 2)(x + 3) = 61
the volume of the container.
x3 + x2 − 6x = 61
21. The product of three consecutive integers is 720. What are the numbers?
22. The height of a box is 3 cm less than the width. The length is 2 cm less than the width.
The volume is 50 cm3. What is the width of the box?
Mrs. Steinberg – Algebra 2