151k views
2 votes
Identifying Roots of a Polynomial: x³ + 2x²-16x-32.

1 Answer

7 votes

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

User Esteban Chornet
by
7.9k points