1.9.1: Review Exercises
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Review Exercises
Real Numbers: Algebra Essentials
For the following exercises, perform the given operations.
(5−3⋅2)2−6
64÷(2⋅8)+14÷7
2⋅52+6÷2
For the following exercises, solve the equation.
5x+9=−11
2y+42=64
For the following exercises, simplify the expression.
9(y+2)÷3⋅2+1
3m(4+7)−m
For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.
11
0
56
√11
Exponents and Scientific Notation
For the following exercises, simplify the expression.
22⋅24
4543
(a2b3)4
6a2⋅a02a−4
(xy)4y3⋅2x5
4−2x3y−32x0
(2x2y)−2
(16a3b2)(4ab−1)−2
Write the number in standard notation: 2.1314×10−6
Write the number in scientific notation: 16,340,000
Radicals and Rational Expressions
For the following exercises, find the principal square root.
√121
√196
√361
√75
√162
√3225
√8081
√491250
24+√2
4√3+6√3
12√5−13√5
5√−243
3√2503√−8
Polynomials
For the following exercises, perform the given operations and simplify.
(3x3+2x−1)+(4x2−2x+7)
(2y+1)−(2y2−2y−5)
(2x2+3x−6)+(3x2−4x+9)
(6a2+3a+10)−(6a2−3a+5)
(k+3)(k−6)
(2h+1)(3h−2)
(x+1)(x2+1)
(m−2)(m2+2m−3)
(a+2b)(3a−b)
(x+y)(x−y)
Factoring Polynomials
For the following exercises, find the greatest common factor.
81p+9pq−27p2q2
12x2y+4xy2−18xy
88a3b+4a2b−144a2
For the following exercises, factor the polynomial.
2x2−9x−18
8a2+30a−27
d2−5d−66
x2+10x+25
y2−6y+9
4h2−12hk+9k2
361x2−121
p3+216
8x3−125
64q3−27p3
4x(x−1)−14+3(x−1)34
3p(p+3)13−8(p+3)43
4r(2r−1)−23−5(2r−1)13
Rational Expressions
For the following exercises, simplify the expression.
x2−x−12x2−8x+16
4y2−254y2−20y+25
2a2−a−32a2−6a−8⋅5a2−19a−410a2−13a−3
d−4d2−9⋅d−3d2−16
m2+5m+62m2−5m−3÷2m2+3m−94m2−4m−3
4d2−7d−26d2−17d+10÷8d2+6d+16d2+7d−10
10x+6y
12a2+2a+1−3a2−1
1d+2c6c+12ddc
3x−7y2x