Select all of the roots of x³ + 2x² - 16x - 32. 
-1, -2, -4, 1, 4, 5

Solution:

Given, the equation is x³ + 2x² - 16x - 32.

We have to find all the roots of the equation.

Taking out common terms,

x³ + 2x² - 16x - 32 = x²(x + 2) - 16(x + 2)

= (x² - 16)(x + 2)

We know, (a²- b²) = (a - b)(a + b)

So, (x² - 16) = (x - 4)(x + 4)

Now, x³ + 2x² - 16x - 32 = (x + 2)(x - 4)(x + 4)

To find the roots,

⇒ (x + 2) = 0

x = -2

⇒ (x - 4) = 0

x = 4

⇒ (x + 4) = 0

x = -4

Therefore, the roots of the equation are -2, -4 and 4.

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Select all of the roots of x³ + 2x² - 16x - 32.

Summary:

The roots of the equation x³ + 2x² - 16x - 32 are -2, -4 and 4.