Using the property of exponents, we have 5^(2 + 3 - 4) = 5^1 = 5.

Using the property of exponents a^m / a^n = a^(m-n), we have 5^(x+1) / 5^(x-1) = 5^((x+1)-(x-1)) = 5^2.

log_2(8) = 3 and log_2(4) = 2, thus log_2(8) + log_2(4) = 3 + 2 = 5.

Substituting x = 1 into P(x) gives P(1) = 1^3 - 3(1^2) + 4 = 2.

Substituting x = 2 into P(x) gives P(2) = 2^3 - 3(2^2) + 4 = 8 - 12 + 4 = 0.

The coefficient of x^2 is given by 4C2 * (3^2) * (-2)^2 = 6 * 9 * 4 = 216.

The coefficient of x^4 in (3x - 2)^6 is given by 6C4 * (3^4) * (-2)^2 = 15 * 81 * 4 = 4860.

The coefficient is C(8,5) * (3^5) * (-2)^3 = 56 * 243 * (-8) = -6720.

Substituting x = 2 into the polynomial gives p(2) = 3(2^2) - 2(2) + 1 = 12 - 4 + 1 = 9.

Substituting x = 2 into the polynomial gives p(2) = 3(2^2) - 4(2) + 1 = 12 - 8 + 1 = 5.

Substituting x = -1 gives P(-1) = 5(-1)^2 - 3(-1) + 7 = 5 + 3 + 7 = 15.

To solve for x, add 9 to both sides and then divide by 3: 3x = 9, thus x = 3.

First, divide both sides by 4: x - 2 = 3, then add 2 to both sides: x = 5.

First, divide both sides by 5: x - 2 = 3. Then add 2 to both sides to find x = 5.

The volume of a cube is given by V = a³. Here, V = 4³ = 64 cm³.

Volume = πr²h = 3.14 * (3)² * 10 = 3.14 * 9 * 10 = 282.6 cm³.

Statistics plays a crucial role in modern mathematics by helping to make inferences and decisions based on data analysis.

The passage states that digital sum helps identify discrepancies in data, making it valuable for error detection.

100 divided by 8 gives 12 with a remainder of 4 (100 - 96 = 4).

1000 divided by 6 gives a remainder of 4.

1000 divided by 9 gives a remainder of 1.

1001 divided by 7 gives 143 with a remainder of 2 (1001 - 7*143 = 2).

256 divided by 11 gives a quotient of 23 and a remainder of 3 (256 - 23*11 = 3).

256 divided by 15 gives a quotient of 17 and a remainder of 1 (256 - 255 = 1).

Multiplying the number by 3 gives (8k + 5) * 3 = 24k + 15, which gives a remainder of 7 when divided by 8.

Since 6 mod 3 = 0, the remainder when the number is divided by 3 is also 0.

The binary system is the foundation of digital electronics and computing, as it represents data in two states.

The binary system is most commonly used in modern computing as it directly corresponds to the on/off states of electronic circuits.

Hexadecimal is most efficient for representing large binary numbers in a compact form, as it condenses four binary digits into one hexadecimal digit.

The hexadecimal system is most efficient for representing large binary numbers due to its compactness.