Question

Which of the following is a polynomial function in standard form with zeros at -8, -1, and 3?

Answer 1

Option A is correct.

Explanation:

Zeros at -8, -1 and 3 means these are the factors of the polynomial.

x=-8, x=-1 and x =3

It can be written as:

x+8=0, x+1=0 and x-3=0

Factors can be written as:

(x+8)(x+1)(x-3)=0

Multiplying the first two terms and then their product with third terms:

`(x(x+1) +8(x+1))(x-3) =0\\(x^2+x+8x+8)(x-3)=0\\Adding\,\, like\,\, terms\,\,:\,\,\\(x^2+9x+8)(x-3) =0\\x(x^2+9x+8) -3(x^2+9x+8)=0\\x^3+9x^2+8x-3x^2-27x-24=0\\Adding\,\, like\,\, terms\,\,:\,\,\\x^3+9x^2-3x^2+8x-27x-24=0\\x^3+6x^2-19x-24=0\\or\,\,f(x) = x^3+6x^2-19x-24`

So, Option A is correct.