Answer:
roots are x = - 4 , x = - 2 , x = 4
Explanation:
given the polynomial
x³ + 2x² - 16x - 32
to find the roots , then equate the polynomial to zero
x³ + 2x² - 16x - 32 = 0 ( factor the first/second and third/fourth terms )
x²(x + 2) - 16(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(x² - 16) = 0 ← x² - 16 is a difference of squares
(x + 2)(x + 4)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 4 = 0 ⇒ x = - 4
x - 4 = 0 ⇒ x = 4
the 3 roots are x = - 4 , x = - 2 , x = 4