The coefficient of x^5 is given by 7C5 * (2)^2 = 21 * 4 = 84.

Determinant of B = (2*7) - (3*5) = 14 - 15 = -1.

Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.

The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.

The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.

f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.

The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

Volume = side³ = 3³ = 27 cubic units.

Volume = πr²h = π(2²)(5) = 20π cubic units.

Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.

Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.

Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.

Setting x = 0, we get -2y = 6, so y = -3.

Setting x = 0, we get -4y = 12, so y = -3.

Setting x = 0 in the equation gives 5y = 20, thus y = 4. The y-intercept is 4.

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 2 - 3i is 2 + 3i.

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 5 - 3i is 5 + 3i.

Substituting (0, -4) into the equation gives 4(0) - 5(-4) + 20 = 0, which is true.