Question

What are the real zeros of the function g(x) = x3 + 2x2 − x − 2? 1, –1, 2 1, –1, –2 1, –1 2, –2, 1

Answer 1

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g(x) = x³ + 2x² - x - 2

To find the zeros or the roots of a function, you need to set the function equal to 0 then solve for x.

x³ + 2x² - x - 2 = 0

Factor left side of the equation

(x + 1)(x - 1)(x + 2) = 0

Now we can set factors equal to 0

x + 1= 0 or x - 1 = 0 or x + 2 = 0

x= 0 - 1 or x = 0 + 1 or x= 0 - 2

x= -1 or x = 1 or x = -2

Thus,

The roots or the zeros of the function are:

-2, -1, 1

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Answer 2

Zeros are x=-2, -1, 1

Explanation:

`g(x) = x^3 + 2x^2 - x -2`

We use grouping method

We group first two terms and last two terms

`g(x) = (x^3 + 2x^2)+(- x -2)`

Factor out GCF from each group

`g(x) = x^2(x+ 2)-1(x +2)`

FActor out x+2

`g(x) =(x+ 2)(x^2-1)`

To find out zeros , set g(x)=0

`0=(x+ 2)(x^2-1)`

Now we set each factor =0 and solve for x

`x+2=0`, x= -2

`x^2-1=0`

`x^2=1`, take square root on both sides

x=1, x=-1

Zeros are x=-2, -1, 1