USE THE METHOD OF DIRECT TO PROVE:
If a is an odd integer, then a’2 + 3a +5 is odd.
Thus a=2c+1a = 2c +1a=2c+1 for some integer c,c,c, by definition of an odd number. Then
where b=2c2+5c+4.b=2c^2+5c+4.b=2c2+5c+4.
Therefore by definition of an odd number, if aaa is an odd integer, then a2+3a+5a^2 + 3a +5a2+3a+5 is odd.
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