Question

A^{3} -7a+18 делится на 3 при каком а?

Answer 1

Ответ:

а должно быть кратно 3

Объяснение:

а³ - 7а + 18 делится на 3 в случае если а³ - 7а делится на 3, так как 18 на 3 делится.

а³ - 7а = а(а² - 7). Значит а должно быть кратно 3. Это может быть 3, 6 или 9 или любое другое число кратное 3

Answer 2

To find the values of "a" for which the expression "A^3 - 7a + 18" is divisible by 3, we need to ensure that the expression leaves a remainder of 0 when divided by 3.

A number is divisible by 3 if and only if the sum of its digits is divisible by 3. In this case, the expression is a polynomial, but we can still use the same concept. The sum of the coefficients of "A^3" and "-7a" is "1 - 7 = -6," and the constant term is "+18." To make the whole expression divisible by 3, the sum of these coefficients must be divisible by 3.

Thus, we have the equation:

(-6 + 18) mod 3 = 0

Solving this equation:

12 mod 3 = 0

So, the expression "A^3 - 7a + 18" is divisible by 3 for all values of "a."