INSTRUCTIONS: Read the references found on the Background Info page. Study the examples there, and the ones given below. Work out the problems, showing all the computational steps. This is particularly important for those problems where the answer is given. On those problems, the correct procedure is the only thing that counts toward the assignment grade.
SOLVING EQUATIONS WITH RADICALS:
Examples: Solve for x. Check by substituting your value for x into the original expression.
Problems:
Solve for x, unless otherwise indicated. Substitute your calculated value into the original expression.
1. Ans: x=36
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
ADDING / SUBTRACTING / MULTIPLYING POLYNOMIALS:
References:
Example:
You are given two polynomials. (Remember that monomials such as 2x and binomials such as 2x+1 are special cases of polynomials). For each problem, calculate the sum, difference and product of the two polynomials.
Problems 16 through 25: Calculate the sum, difference and product of the two polynomials.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
— end —
5×6
=
2×8
=
2
x8
3
=
3
x8
=
3×16
-=
3
4
vx
3
p
=
3
4
x27
=
3×69
-=
2×7811
-+=
x
2a
2
=
5xx12
=-
1A
R Solve for A.
2
p
=
3V
R Solve for V.
H
p
=
x4y2 Solve for x.
+=+
2
22
2
22
2
23
3
22
232
2
322
3432
E4:
x:x1
sum:(x)(x1)(xx1)
ANS:(xx1)
diff:(x)(x1)(xx1)
ANS:(xx1)
prod:(x)(x1)(xx)
ANS:(xx)
11.x:x1
12.2×1:xx2x1
13.3x:x3x2
14.x2x3x1:xx4
15.x2x5:xx3x2x
–
+-=+-
+-
–=-++
-++
-=-
–
–
–+-
-+
-+–+
+–+-+
3
x:x1
–
x:y1
–
x1:x2
—
2
x:x
2
x1:x2
—
22
x:x1
–
232
2×1:xx2x1
–+-
2
3x:x3x2
-+
322
x2x3x1:xx4
-+–+
3432
x2x5:xx3x2x3
+–+-+
(
)
(
)
(
)
2
2
2
2
2
2
2
E1.x2
x2
x4
Ans: x4
Checking: 42
E2.x14
x14
x116
x16117
Ans: x17
Checking: 171164
E2.Ax
A
x
A
x
A
Ans: x
AA
Checking: A
p
p
p
p
pp
pp
=
=
=
=
=
-=
-=
-=
=+=
=
-==
=
=
=
=
æö
æö
==
ç÷
ç÷
ç÷
èø
èø
x6
=
