$$2x - (3y + 1) = 2(4) - (3 \times 2 + 1) = 8 - (6 + 1) = 8 - 7 = 1$$

Question 1

Which of the following is an algebraic expression, and why?

Accepted Answer

$$2x + 5$$ because it contains a variable and operations.

Question 2

Evaluate the algebraic expression $$2x - (3y + 1)$$ when $$x = 4$$ and $$y = 2.$$

Accepted Answer

$$2x - (3y + 1) = 2(4) - (3 	imes 2 + 1) = 8 - (6 + 1) = 8 - 7 = 1$$

Question 3

Simplify the expression $$-3(5 + 4x - y - 7).$$

Accepted Answer

$$-15 - 12x + 3y + 21$$

Question 4

Which of the following is the standard form of the polynomial $$5x^2$$ + $$3x^4 + 4$?

Accepted Answer

$$3x^4$$ + $$5x^2 + 4$

Question 5

Add the polynomials: $$(4x^2 - 7x$$) + $$2x^2$$ - $$5x^2 + 9x + 4$

Accepted Answer

Question 6

Multiply the polynomials using FOIL: $$(x + 2)(x + 3)$$

Accepted Answer

$$x^2 + 5x + 6$

Question 7

Simplify the expression using exponent rules: $$\dfrac{-5a^7$b^3$$}{$$-5a^2b^5$}$$

Accepted Answer

$$a^5b$$^{-2}$

Question 8

Rewrite the expression $$\dfrac{4x^2$y^3$$}{$$y^2$$}$ using exponent rules.

Accepted Answer

$$4x^2y$

Question 9

Simplify the radical $$\sqrt{75}.$$

Accepted Answer

$$5\sqrt{3}$$

Question 10

Rationalize the denominator and simplify: $$\dfrac{6 + \sqrt{5}}{\sqrt{5}}$$

Accepted Answer

$$\dfrac{6\sqrt{5} + 5}{5}$$

Question 11

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x - 5)(x + 3)$$

Question 12

Simplify the radical $$\sqrt{180}.$$

Accepted Answer

$$6\sqrt{5}$$

Question 13

Which of the following is the result of multiplying $$(x + 3)(x - 5)(x - 2 + 1)$$?

Accepted Answer

$$(x + 3)(x - 5)(x - 1)$$

Question 14

Rewrite $$\sqrt[3]{8x^6$} in $$simplest form.

Accepted Answer

$$2x^2$$

Question 15

Which of the following is the correct simplification of $$\dfrac{-12b$$^{11}$$}{48b^7$}$$?

Accepted Answer

$$-\dfrac{1}{4}b^4$

Question 16

Which of the following is the correct factorization of $$25x^2 - 110x + 121$?

Accepted Answer

$$(5x - 11)^2$

Question 17

Simplify the expression $$\left(\dfrac{x^3$y^2$$}{$$z^4$$}\$$right)^2$ using exponent rules.

Accepted Answer

$$\dfrac{x^6$y^4$$}{$$z^8$$}$

Question 18

Which of the following is the correct simplification of $$\sqrt{(5 - 3)^2$}$$?

Accepted Answer

$$2$$

Question 19

True or False: $$\sqrt{11}$$ and $$\sqrt{121}$$ are equal.

Accepted Answer

False

Question 20

Which of the following is the correct rational exponent form for $$\sqrt[5]{a^3$}$$?

Accepted Answer

$$a^{3/5}$$

Precalculus Study Notes: Review of Basic Concepts (Algebraic Expressions, Polynomials, Exponents, and Radicals)

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