Question

How do you find the zeros of the polynomial function with equation `f(x)=x^3+8x^2-x-8`?

Answer 1

x = -8 , x = ± 1

Explanation:

The zeros are the values of x , which make the function equal zero.

ie `x^3 + 8x^2 - x - 8 = 0`

To solve this equation for x , require to factorise it.

Consider the function 'split' into 2 pairs of terms.

hence `[ x^3 + 8x^2 ] + [-x - 8 ]`

now factor each pair

thus `x^2(x + 8) - 1(x+8) = (x + 8)(x^2 - 1)`

`rArr (x+8)(x^2-1) = 0`

solve x + 8 = 0 → x = -8

solve `x^2 -1 = 0 → (x+1)(x-1) = 0 → x = ± 1`