Q: Which of the following is the correct prime factorization of $$45 \times 20$$?

$$3^2$$ \times 5 \times $$2^2$$ \times 5$$

Q: Which of the following is the correct prime factorization of $$24 \cdot 18 \cdot 30$$?

$$2^3$$ \times 3 \times 2 \times $$3^2$$ \times 2 \times 3 \times 5$$

Question 1

Which of the following expressions is undefined?

Accepted Answer

$$\frac{45}{0}$$

Question 2

Evaluate $$|-3|^2.$$

Accepted Answer

$$9$$

Question 3

Simplify the expression: $$6 + 4| -3 |.$$

Accepted Answer

$$18$$

Question 4

Which of the following is the correct prime factorization of $$45 	imes 20$$?

Accepted Answer

$$3^2$$ 	imes 5 	imes $$2^2$$ 	imes 5$$

Question 5

Solve for $$x$$: $$2x + 3x = 12.$$

Accepted Answer

Question 6

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{80}$$

Question 7

Write $$\frac{18}{27} in $$lowest terms using factoring.

Accepted Answer

Question 8

If $$x is a $$number, which equation represents 'Five less than a number is one hundred'?

Accepted Answer

$$x - 5 = 100$$

Question 9

Evaluate $$(-1)^{100}.$$

Accepted Answer

$$1$$

Question 10

Given $$a = 1$$, $$b = 5$$, evaluate $$a^2$$ + $$b^2.$$

Accepted Answer

$$26$$

Question 11

Simplify $$2x - 4x + 6x.$$

Accepted Answer

Question 12

If $$x is a $$number, which equation represents 'Double the sum of a number and eleven equals 24'?

Accepted Answer

$$2(x + 11) = 24$$

Question 13

Evaluate $$|4 - 7|.$$

Accepted Answer

$$3$$

Question 14

Simplify $$-4 + 3^2$.

Accepted Answer

$$5$$

Question 15

If $$x = -2$$, $$y = -1$$, evaluate $$3x^2$$|x - y|$$.

Accepted Answer

$$36$$

Question 16

Which of the following is the correct prime factorization of $$24 \cdot 18 \cdot 30$$?

Accepted Answer

$$2^3$$ 	imes 3 	imes 2 	imes $$3^2$$ 	imes 2 	imes 3 	imes 5$$

Question 17

Solve for $$x$$: $$8x = 56.$$

Accepted Answer

$$x = 7$$

Question 18

Simplify $$-5^2$$ + $$2^4$$ - |-2|^4$$.

Accepted Answer

$$-25 + 16 - 16 = -25$$

Question 19

Which equation represents 'The sum of twice a number and four is negative six'?

Accepted Answer

$$2x + 4 = -6$$

Question 20

If Elizabeth has a 96-inch ribbon to be cut into three pieces, the longest piece is three times the shortest, and the third piece is six inches more than twice the shortest, what is the length of the shortest piece?

Accepted Answer

$$12$$ inches

College Algebra: Fundamental Concepts and Problem Solving

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