CSET CSET Mathematics: Number Theory and Algebra

Question 1

Which of the following is the prime factorization of 360?

Accepted Answer

2³ × 3² × 5

Answer

360 = 8 × 45 = 2³ × 3² × 5.

Question 2

What is the greatest common divisor (GCD) of 84 and 120?

Accepted Answer

24

Answer

Using the Euclidean algorithm: GCD(120, 84) = GCD(84, 36) = GCD(36, 12) = 12... wait, GCD(84,120): 120=1×84+36, 84=2×36+12, 36=3×12+0, so GCD=12.

Question 3

Which property is illustrated by a(b + c) = ab + ac?

Accepted Answer

Distributive property

Answer

The distributive property states that multiplication distributes over addition: a(b + c) = ab + ac.

Question 4

If f(x) = 3x² − 2x + 1, what is f(−2)?

Accepted Answer

17

Answer

f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.

Question 5

Which of the following sets is closed under multiplication?

Accepted Answer

Even integers

Answer

Even integers are closed under multiplication because the product of any two even integers is always even.

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