Question 1

Simplify the following expression without using a calculator: $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 2

Which of the following is the correct factorization of $$x^2 - 16$ over the real numbers?

Accepted Answer

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

Question 3

Solve the equation $$x^2 - x - 12 = 0$ by factoring.

Accepted Answer

$$x = 4 or$$ $$x = -3$$

Question 4

Which of the following is the correct solution to $$(x-2)^2 = 75$ using the square root property?

Accepted Answer

$$x = 2 \pm 5\sqrt{3}$$

Question 5

Distribute and simplify: $$-5x^2(3x - 5$$)$$.

Accepted Answer

$$-15x^3$$ + $$25x^2$$

Question 6

Factor the following completely over the real numbers: $$x^3 - 8$.

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 7

Solve the equation $$x^2 + 3x - 10 = 0$ using the quadratic formula.

Accepted Answer

$$x = 2 or$$ $$x = -5$$

Question 8

Which of the following is the correct factorization of $$25x^2 - 49$?

Accepted Answer

$$(5x + 7)(5x - 7)$$

Question 9

Solve $$x^2 = 81$ using the square root property.

Accepted Answer

$$x = 9 or$$ $$x = -9$$

Question 10

Which of the following is the correct solution to $$x^2 + 25 = 0$ over the real numbers?

Accepted Answer

Not factorable over the real numbers

Question 11

Solve $$x^2 - 8x + 10 = 0$ using the quadratic formula.

Accepted Answer

$$x = 4 \pm \sqrt{6}$$

Question 12

Factor the following polynomial: $$3x^3$$ - $$60x^2 + 300x$.

Accepted Answer

$$3x(x^2 - 20x + 100$$)$$

Question 13

Solve $$x^3 - 121x = 0$ by factoring.

Accepted Answer

$$x = 0$$, $$x = 11$$, $$x = -11$$

Question 14

Complete the square to solve $$x^2 - 6x + 4 = 0$.

Accepted Answer

$$x = 3 \pm \sqrt{5}$$

Question 15

Which of the following is the correct expansion of $$(2x^3$$ + $$7)^2$$?

Accepted Answer

$$4x^6$$ + $$28x^3 + 49$

Question 16

Solve $$5x^2 + 40x - 25 = 0$ by completing the square.

Accepted Answer

$$x = -4 \pm \sqrt{5}$$

Question 17

Factor $$x^2 + 4x - 32$ over the real numbers.

Accepted Answer

$$(x + 8)(x - 4)$$

Question 18

Solve $$x^2 - 4 = 0$ using the square root property.

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 19

Which of the following is the correct factorization of $$x^2 + 25$ over the real numbers?

Accepted Answer

Not factorable over the real numbers

Pre-Calculus Review for Calculus Preparation: Step-by-Step Guidance

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