Question

You are told that a third powered polynomial has zeroes at -1, 2, 5.

Part A. Write the three factors of the polynomial

Part B. Write the polynomial in standard form

Answer 1

a) factors of polynomial are: (x+1)(x-2)(x-5)

b) the required polynomial in standard form is:
`\mathbf{x^3-6x^2+3x+10}`

Explanation:

The polynomial has zeros at -1,2,5

Part A) Write the three factors of the polynomial

we have x=-1, x=2 and x=5 as zeros of polynomial

so factors will be:

(x+1)=0, (x-2)=0, (x-5)=0

So, factors of polynomial are: (x+1)(x-2)(x-5)

Part B) Write the polynomial in standard form

For finding polynomial, we will multiply all the factors i.e

(x+1)(x-2)(x-5)

`(x+1)(x-2)(x-5)\\=(x(x-2)+1(x-2))(x-5)\\=(x^2-2x+x-2)(x-5)\\=(x^2-x-2)(x-5)\\=x(x^2-x-2)-5(x^2-x-2)\\=x^3-x^2-2x-5x^2+5x+10\\=x^3-x^2-5x^2+5x-2x+10\\=x^3-6x^2+3x+10`

So, the required polynomial in standard form is:
`x^3-6x^2+3x+10`