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

Answer:

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.