Review Exercises
Real Numbers: Algebra Essentials
For the following exercises, perform the given operations.
64÷(2⋅8)+14÷7
For the following exercises, solve the equation.
5x+9=−11
For the following exercises, simplify the expression.
9(y+2)÷3⋅2+1
For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.
11
56
Exponents and Scientific Notation
For the following exercises, simplify the expression.
22⋅24
(a2b3)4
(xy)4y3⋅2x5
(2x2y)−2
Write the number in standard notation: 2.1314×10−6
Radicals and Rational Expressions
For the following exercises, find the principal square root.
√121
√361
√162
√8081
24+√2
12√5−13√5
3√2503√−8
Polynomials
For the following exercises, perform the given operations and simplify.
(2y+1)−(2y2−2y−5)
(6a2+3a+10)−(6a2−3a+5)
(2h+1)(3h−2)
(m−2)(m2+2m−3)
(x+y)(x−y)
Factoring Polynomials
For the following exercises, find the greatest common factor.
12x2y+4xy2−18xy
For the following exercises, factor the polynomial.
2x2−9x−18
d2−5d−66
y2−6y+9
361x2−121
8x3−125
4x(x−1)−14+3(x−1)34
4r(2r−1)−23−5(2r−1)13
Rational Expressions
For the following exercises, simplify the expression.
4y2−254y2−20y+25
d−4d2−9⋅d−3d2−16
4d2−7d−26d2−17d+10÷8d2+6d+16d2+7d−10
12a2+2a+1−3a2−1
3x−7y2x