James Stewart, CALCULUS Concepts & Contexts 4th edition
Download the Diagnostic Test of Algebra Solutions Step by Step
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6. Rationalize the expression and simplify.
7. Rewrite by completing the square.
8. Solve the equation. (Find only the real solutions.)
9. Solve each inequality. Write your answer using interval notation.
1. Evaluate each expression without using a calculator.
a) (-3) ^4 =
b) -3^4 =
c) 3^-4 =
d) {5^{23}} over {5^{21}} =
e) ({2} over {3} )^{-2} =
f) 16^{-3 / 4 } =
2. Simplify each expression. Write your answer without negative exponents.
a) sqrt{200} - sqrt{32} =
b) (3a^{3}b^{3}) (4ab^{2})^{2} =
c) ({3x^{3 / 2 }y^{3}} over {x^{2} y^{-1 /2 }} )^{-2} =
3. Expand and simplify.
a) 3(x + 6) + 4(2x - 5) =
b) (x + 3)(4x - 5) =
c) (sqrt{a} + sqrt{b}) (sqrt{a} - sqrt{b}) =
d) (2x + 3) ^{2} =
e) (x + 2)^{3} =
4. Factor each expression.
a) (4x^{2} - 25) =
b) 2x^{2} + 5x -12 =
c) x^{3} - 3x^{2} - 4x + 12 =
d) x^{4} + 27x =
e) 3x^{{3} over {2}} - 9x^{{1} over {2}} + 6x^-{{1} over {2}} =
f) x^{3} y - 4xy =
5. Simplify the rational expression.
a) {x^{2} + 3x + 2} over {x^{2} - x - 2} =
b) {2x^{2} - x - 1} over {x^{2} - 9} cdot {{x + 3} over {2x + 1}} =
c) {x^{2}} over {x^{2} - 4} - {{x + 1} over {x + 2}} =
d) {{y} over {x} - {x} over {y}} over {{1} over {y} - {1} over {x}} =
6. Rationalize the expression and simplify.
a) {sqrt{10} } over {sqrt{5} - 2} =
b) {sqrt{4 + h} - 2} over {h} =
7. Rewrite by completing the square.
a) x^{2} + x + 1 =
b) 2x^{2} - 12x + 11 =
8. Solve the equation. (Find only the real solutions.)
a) x + 5 = 14 - 1 / 2
b) {2x} over {x + 1} = {2x - 1} over {x}
c) x^{2} - x - 12 =
d) 2x^{2} + 4x + 1 =
e) x^{4} - 3x^2 + 2 = 0
f) 3 lline x - 4 rline = 10
g) 2x(4 - x)^-({1} over {2}) - 3 sqrt{4 - x} =
9. Solve each inequality. Write your answer using interval notation.
a) -4 <>
b) x^2 <>
c) x (x - 1)(x + 2) > 0
d) lline x - 4 rline <>
10. State whether each equation is true or false.
e) {2x - 3} over {x + 1}
10. State whether each equation is true or false.
a) ( p + q )^2 = p^2 + q^2 =
b) sqrt{ab} = sqrt{a} sqrt{b} =
c) sqrt{a^2 + b^2} = a + b
d) {1 + TC} over {C} = 1 + T =
e) {1} over {x - y} = {1} over {x} - {1} over {y} =
f) {{1} over {x} } over {{a} over {x} - {b} over {x}} =
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