Answer:
a optionis a correct answer
Answer:
(x+3)( 3x^2 +5)
Step-by-step explanation:
3x^3+9x^2+5x+15
Split into two groups
3x^3+9x^2 +5x+15
Factor 3x^2 out of the first group and 5 out of the second group
3x^2 ( x+3) + 5(x+3)
Factor out x+3
(x+3)( 3x^2 +5)
Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
P(A) means "Probability of Event A" The complement is shown by a little mark after the letter such as A' (or sometimes Ac or A): P(A') means "Probability of the complement of Event A" The two probabilities always add to 1.