Question

What are the zeros of the polynomial function?

Answer 1

-2, -2, 1

Explanation:

simply substitute each potential answer into f(x) and see which one results in f(x) = 0,

f(x) = x³ + 2x² - x - 2

f(-3) = (-3)³ + 2(-3)² - (-3) - 2 = -8(not a root)

f(-2) = (-2)³ + 2(-2)² - (-2) - 2 = 0(Is a root!)

f(-1) = (-1)³ + 2(-1)² - (-1) - 2 = 0 (Is a root!)

f(0) = (0)³ + 2(0)² - (0) - 2 = -2 (not a root)

f(1) = (1)³ + 2(1)² - (1) - 2 = 0(Is a root!)

f(2) = (2)³ + 2(2)² - (2) - 2 = 12(not a root)

f(3) = (3)³ + 2(3)² - (3) - 2 = 40(not a root)

Answer 2

-1

1

2

Explanation:

x³+2x²-x-2=(x²-1)(x-2)

(x²-1)(x-2)=0

x²-1=0

x-2=0

x12=√1

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x1=-1

x2=1

x3=2

x