Exercise Set 4.4: Using Factoring to Solve Equations
Math 1300, Fundamentals of Mathematics
The University of Houston Chapter 4: Factoring
Solve the following equations by factoring.
1. 02110
2=+− xx
2. 04013
2=++ xx
3. 0128
2=++ xx
4. 0406
2=−− xx
5. 35)2( =−xx
6. 20)8( =+xx
7. 7214
2=+ xx
8. xx 1160
2=−
9. 01572 2=−− xx
10. 0473 2=+− xx
11. 12176 2−=+ xx
12. 6710 2=− xx
13. 253 2−=− xx
14. 0568 2=−− xx
15. 025
2=−x
16. 049
2=−x
17. 094 2=−x
18. 02536 2=−x
Solve the following equations by factoring. To simplify
the process, remember to first factor out the Greatest
Common Factor (GCF) and to factor out a negative if
the leading coefficient is negative.
19. 08
2=− xx
20. 010
2=+ xx
21. 25360xx−− + =
22. 214 48 0xx−− − =
23. 0213 2=+− xx
24. 0305 2=− xx
25. 0123 2=−x
26. 077 2=+− x
27. 090155 2=+−− xx
28. 024204 2=++− xx
29. 03023080 2=−+ xx
30. 0187512 2=+− xx
31. 32
560xxx
+
+=
32. 32
7180xx x
−
−=
Each of the quadratic functions below is written in the
form 2
()fx ax bx c
=
++
. The graph of a quadratic
function is a parabola with vertex, where 2
b
a
h=
−
and
(
)
2
b
a
kf=−.
(a) Find the x-intercept(s) of the parabola by
setting () 0fx
=
and solving for x.
(b) Write the coordinates of the x-intercept(s)
found in part (a).
(c) Find the y-intercept of the parabola and write
its coordinates.
(d) Give the coordinates of the vertex (h, k) of the
parabola, using the formulas 2
b
a
h=
−
and
(
)
2
b
a
kf=−.
(e) Does the parabola open upward (with the
vertex being the lowest point on the graph) or
downward (with the vertex being the highest
point on the graph)?
(f) Find the axis of symmetry. (Be sure to write
your answer as an equation of a line.)
(g) Draw a graph of the parabola that includes
the features from parts (b) through (e).
33. 2
() 6 8fx x x
=
−+
34. 2
() 2 15fx x x
=
−−
35. 2
() 8 16fx x x
=
−+
36. 2
( ) 10 16fx x x
=
−+ −
37. 2
() 4 21fx x x
=
−− +
38. 2
() 10 25fx x x
=
++
39. 2
() 3 12 36fx x x
=
+−
40. 2
() 4 8 5fx x x
=
−−+
