Its for exam review pls show step by stepSolution1 x3 48x

It\'s for exam review pls show step by step

Solution

1) x³ - 48x - 128 can be written as : (x - 8)(x² + 8x + 16) = (x - 8)(x + 4)²

therefore the solutions for this cubic equation are : x = 8 and x = -4

since k = -4, the answer is C].

2) 8x³ + 34x² + 27x - 9 can be written as: (4x - 1)g(x) = 8x³ + 34x² + 27x - 9 [since we are given that x = 1/4 is a root]

therefore if we divide f(x) by 4x - 1, we get: g(x) = 2x² + 9x + 9 = (2x + 3)(x + 3)

therefore f(x) = (4x - 1)(2x + 3)(x + 3) [option B].

3) We are given that (1 + i) is a root of the equation. Thus (1 - i) will also be a root of the equation.

So, our f(x) can be written as: x³ + 3x² - 8x + 10 = ( x - (1 + i))(x - (1 - i)) g(x)

=> x³ + 3x² - 8x + 10 = (x - 1 - i)(x - 1 + i)g(x)

=> x³ + 3x² - 8x + 10 = (x² - 2x + 3)g(x)

If we divide the two, we get g(x) = x + 5

therefore the roots are (1 + i), (1 - i) and (x + 5)

4) -2x⁴ + 4x³ + 6x² + 18 =