Q23 of 47 Page 172

Find all integers n for which the number (n + 3)(n – 1) is also an integer.

Let n = 0


= (0 + 3)(0-1)


= (3)(-1)


= -3 which is also an integer


Let n = -1


= (-1 + 3)(-1-1)


= (2)(-2)


= -4 which is also an integer


Let n = 1


= (1 + 3)(1-1)


= (4)(0)


= 0, which is also an integer


Therefore, for any integer value of n the equation will result an integer.


More from this chapter

All 47 →
19

Find all integers such that is also an integer.

 20

By inserting parenthesis (that is brackets), you can get several values for 2 × 3 + 4 × 5. (For example ((2 × 3) + 5 is one way of inserting parenthesis.) How many such values are there?

 21

Suppose is a positive rational in its lowest form. Prove that is also in its lowest form.

22

Show that for each natural number n, the fraction is in its lowest form.