Ch. P - Fundamental Concepts of Algebra
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- Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4
Problem 1
- In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x^2−5
Problem 1
- In Exercises 1–10, factor out the greatest common factor. 18x+27
Problem 1
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)
Problem 1
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x^2−25)
Problem 3
- Evaluate each exponential expression in Exercises 1–22. (−2)^6
Problem 3
- In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x
Problem 3
- In Exercises 1–10, factor out the greatest common factor. 3x^2+6x
Problem 3
- Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∩ B.
Problem 4
- Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.
Problem 5
- In Exercises 5–8, find the degree of the polynomial. 3x^2−5x+4
Problem 5
- In Exercises 1–10, factor out the greatest common factor. 9x^4−18x^3+27x^2
Problem 5
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x^2+11x+10)
Problem 5
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25
Problem 6
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x^2−6x+9)
Problem 7
- In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63
Problem 7
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25
Problem 8
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
Problem 9
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)
Problem 9
- Rewrite each expression without the absolute value bars. |√2-1|
Problem 10
Problem 10
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25
- Evaluate each exponential expression in Exercises 1–22. 4^−3
Problem 11
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (y^2+7y−18)/(y^2−3y+2)
Problem 11
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (17x^3−5x^2+4x−3)−(5x^3−9x^2−8x+11)
Problem 11
- Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.
Problem 12
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2
Problem 12
- In Exercises 11–16, factor by grouping. x^3−3x^2+4x−12
Problem 12
- State the name of the property illustrated: 3+17 = 17+3
Problem 13
- Evaluate each exponential expression in Exercises 1–22. 2^2⋅2^3
Problem 13
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x^2−7x−8)+(2x^2−3x+7)−(x^2−4x−3)
Problem 13
