Question 1

Which of the following is an algebraic expression?

Accepted Answer

$$2x + 5$$

Question 2

Evaluate the expression $$4x - 3y$$ when $$x = 2$$ and $$y = -1.$$

Accepted Answer

$$8$$

Question 3

Simplify the expression $$3x + 4x^2$ - 2x + 5 - x^2$.

Accepted Answer

$$2x^2 + x + 5$

Question 4

Which rule allows you to simplify $$(a^3)^4$?

Accepted Answer

Power Rule

Question 5

Simplify the expression $$\frac{6x^5$y^3$$}{$$2x^2y$$}$.

Accepted Answer

$$3x^3y^2$

Question 6

Which of the following is a trinomial?

Accepted Answer

$$x^2 + 2x + 1$

Question 7

Write $$\sqrt[3]{x^6$} in $$simplest form, assuming $$x is $$positive.

Accepted Answer

$$x^2$$

Question 8

What is the result of multiplying $$(x + 2)(x - 3)$$ using the FOIL method?

Accepted Answer

$$x^2 - x - 6$

Question 9

Factor the polynomial $$x^2 - 16$ completely.

Accepted Answer

$$(x + 4)(x - 4)$$

Question 10

Rationalize the denominator: $$\frac{5}{\sqrt{2}}.$$

Accepted Answer

$$\frac{5\sqrt{2}}{2}$$

Question 11

Which of the following is NOT a polynomial?

Accepted Answer

$$2x^{-1} + 5$

Question 12

Simplify $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 13

If $$a = 2$$ and $$b = -3$$, evaluate $$2a^2 - 3b$.

Accepted Answer

$$17$$

Question 14

Which of the following is the conjugate of $$3 + \sqrt{5}$$?

Accepted Answer

$$3 - \sqrt{5}$$

Question 15

Rewrite $$\sqrt[4]{x^8$}$$ using exponents.

Accepted Answer

$$x^2$$

Question 16

Which property is used to simplify $$\frac{a^7$}{a^3$}$$?

Accepted Answer

Quotient Rule

Question 17

Factor $$x^2 + 7x + 12$ using the AC method.

Accepted Answer

$$(x + 3)(x + 4)$$

Question 18

Simplify $$\$$left(2x^3$$y^2$$\$$right)^2$.

Accepted Answer

$$4x^6y^4$

Question 19

Which of the following is the correct simplification of $$\sqrt{18x^2$}$$, assuming $$x is $$positive?

Accepted Answer

$$3x\sqrt{2}$$

Question 20

A right triangle has legs of length $$6$$ and $$8. $$What is the length of the hypotenuse?

Accepted Answer

$$10$$

Fundamental Concepts of Algebra: Precalculus Study Notes

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