Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Divide using long division. Check your answers.
-
(
x
2
−
3
x
−
40
)
÷
(
x
+
5
)
open , x squared , minus 3 x minus 40 close divides open x plus 5 close
-
(
3
x
2
+
7
x
−
20
)
÷
(
x
+
4
)
open 3 , x squared , plus 7 x minus 20 close divides open x plus 4 close
-
(
x
3
+
3
x
2
−
x
+
2
)
÷
(
x
−
1
)
open , x cubed , plus , 3 x squared , minus x plus 2 close divides open x minus 1 close
-
(
2
x
3
−
3
x
2
−
18
x
−
8
)
÷
(
x
−
4
)
open 2 , x cubed , minus , 3 x squared , minus 18 x minus 8 close divides open x minus 4 close
-
(
3
x
3
+
9
x
2
+
8
x
+
4
)
÷
(
x
+
2
)
open 3 , x cubed , plus , 9 x squared , plus 8 x plus 4 close divides open x plus 2 close
-
(
9
x
2
−
21
x
−
20
)
÷
(
x
−
1
)
open 9 , x squared , minus 21 x minus 20 close divides open x minus 1 close
-
(
x
2
−
7
x
+
10
)
÷
(
x
+
3
)
open , x squared , minus 7 x plus 10 close divides open x plus 3 close
-
(
x
3
−
13
x
−
12
)
÷
(
x
−
4
)
open , x cubed , minus 13 x minus 12 close divides open x minus 4 close
See Problem 2.
Determine whether each binomial is a factor of
x
3
+
4
x
2
+
x
−
6
.
x cubed , plus 4 , x squared , plus x minus 6 .
-
x
+
1
x plus 1
-
x
+
2
x plus 2
-
x
+
3
x plus 3
-
x
−
3
x minus , 3
See Problem 3.
Divide using synthetic division.
-
(
x
3
+
3
x
2
−
x
−
3
)
÷
(
x
−
1
)
open , x cubed , plus , 3 x squared , minus x minus 3 close divides open x minus 1 close
-
(
x
3
−
4
x
2
+
6
x
−
4
)
÷
(
x
−
2
)
open , x cubed , minus , 4 x squared , plus 6 x minus 4 close divides open x minus 2 close
-
(
x
3
−
7
x
2
−
7
x
+
20
)
÷
(
x
+
4
)
open , x cubed , minus , 7 x squared , minus 7 x plus 20 close divides open x plus 4 close
-
(
x
3
−
3
x
2
−
5
x
−
25
)
÷
(
x
−
5
)
open , x cubed , minus , 3 x squared , minus 5 x minus 25 close divides open x minus 5 close
-
(
x
2
+
3
)
÷
(
x
−
1
)
open , x squared , plus 3 close divides open x minus 1 close
-
(
3
x
3
+
17
x
2
+
21
x
−
9
)
÷
(
x
+
3
)
open 3 , x cubed , plus , 17 x squared , plus 21 x minus 9 close divides open x plus 3 close
-
(
x
3
+
27
)
÷
(
x
+
3
)
open , x cubed , plus 27 close divides open x plus 3 close
-
(
6
x
2
−
8
x
−
2
)
÷
(
x
−
1
)
open 6 , x squared , minus 8 x minus 2 close divides open x minus 1 close
See Problem 4.
Use synthetic division and the given factor to completely factor each polynomial function.
-
y
=
x
3
+
2
x
2
−
5
x
−
6
;
(
x
+
1
)
y equals , x cubed , plus 2 , x squared , minus 5 x minus 6 semicolon open x plus 1 close
-
y
=
x
3
−
4
x
2
−
9
x
+
36
;
(
x
+
3
)
y equals , x cubed , minus , 4 x squared , minus 9 x plus 36 semicolon open x plus 3 close
-
Geometry The volume, in cubic inches, of the decorative box shown can be expressed as the product of the lengths of its sides as
V
(
x
)
=
x
3
+
x
2
−
6
x
.
v open x close equals , x cubed , plus , x squared , minus 6 x . What linear expressions with integer coefficients represent the length and height of the box?