a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let
- Taken mod 3, the last two terms vanish, and
so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since 
, we multiply the first term by 2.
- Taken mod 4, the first and last terms vanish, and
. Multiply by the inverse of 3 modulo 4 (which is 3 because 
), then by 2 to ensure the proper remainder is left.
- Taken mod 5, the first two terms vanish, and
. Multiply by the inverse of 2 modulo 5 (3, since 
) and again by 3.
By the CRT, we have
i.e. any number 
(where 
is an integer) satisifes the system.
b. The moduli are not coprime, so we need to check for possible contradictions. If 
and 
, then we need to have 
. This basically amounts to checking that if , then we should also have 
.
The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.
Answer:
1
Step-by-step explanation:
The synthetic division tableau and instructions for its use are shown in the attachment. The number at top left (1) is the zero of the divisor, the opposite of the constant -1.
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<em>Additional comment</em>
Essentially, you're evaluating the function for x=1. The synthetic division is a long way to get the sum of coefficients, which is what the function value is when x=1.
3 -2 +1 -1 = 1
Answer:
60/100
Step-by-step explanation:
We know that 20 goes into 100 5 times, so we multiple numerator and denominator by 20 to get an equivalent fraction:
This would be -14 and -1 (I'm assuming you're trying to factor a quadratic equation).
Check:
-14*-1=14
-14-1=-15
Answer: median
Step-by-step explanation:
