Question

What is f(x)=x3+2x2−5x−6 in factored form given that 2 is a zero of the function?

Answer 1

`x^(3)+2x^(2) -5x-6`

Horner:

2 1 2 -5 -6

1 4 3 0

`x^(3)+2x^(2) -5x-6`=
`(x-2)(x^(2) +4x+3)`

g(x)=
`x^(2) +4x+3`

g(-1)=0

Horner

-1 1 4 3

1 3 0

`x^(2) +4x+3`=(x+1)(x+3)

`f(x)=x^(3)+2x^(2) -5x-6=(x-2)(x+1)(x+3)`

Answer 2

Since 2 or x-2= 0 is a zero of the function we divide it by the function to get the other factors

x³ + 2x² - 5x - 6 ÷ x -2

We get

(x + 3)(x+1) = 0

Therefore x³ + 2x² - 5x - 6 in factored form is

(x - 2)(x + 3)(x + 1)

Hope this helps.