Hi guys I was able to answer this question using trial and error. Was hoping you guys can give me a more mathematical way of arriving at the answer thanks.
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r
1) When t is divided by 7 the remainder is 6
2) When t^2 is divided by 7 the remainder is 1
I broke down the given polynomial in the question stem to arrive at
(t+3)(t+2) . So from number 1 we can tell that t+1 is divisible by 7 then I proceeded to use different values . I'm sure you guys can come up with a better way to solve this.
The answer to the question is A by the way
(t+3)(t+2) = 7*q+r
S1. t = 7m+6
(7m+6+3)(7m+6+2) = (7m+9)(7m+8) => 72/7 r=2 : sufficient
S2. t^2 = 7n+1
t^2-1 = 7n
(t+1)*(t-1) = 7n tells that either t+1 or t-1 is multiple of 7
1. t=7k+1 or 2. t=7k-1
1. (7k+1+3)(7k+1+2)=(7k+4)(7k+3) => 12/7 r=5
2. (7k-1+3)(7k-1+2) = (7k+2)(7k+1) => 2/7 r=2
A it is.
The only thing that matters is what you believe.