Question

Consider the statement "2 is a factor of n2 + 3n."

If n = 1, the statement is "2 is a factor of __________."
If n = 2, the statement is "2 is a factor of __________."
If n = 3, the statement is "2 is a factor of __________."
If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________."
If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."

4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8

4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7

4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4

Answer 1

Answer:

The answer is the last one:

4 , 10 , 18 , (k + 1)² + 3(k + 1) and k² + 5k + 4

Step-by-step explanation:

∵ 2 is a factor of n² + 3n

∵ n = 1 ⇒ ∴ (1)² + 3(1) = 1 + 3 = 4 ⇒ 2 is a factor of 4

∵ n = 2 ⇒ ∴ (2)² + 3(2) = 4 + 6 = 10 ⇒ 2 is a factor of 10

∵ n = 3 ⇒ ∴ (3)² + 3(3) = 9 + 9 = 18 ⇒ 2 is a factor of 18

∵ n = k + 1 ⇒ ∴ (k + 1)² + 3(k + 1) ⇒ before the simplify

∵ n = k + 1 ⇒ ∴ k² + 2k + 1 + 3k + 3 = k² + 5k + 4 ⇒ after simplify