Question

Find a polynomial function of degree 3 with the given numbers as zeros. Assume that the leading coefficient is 1.

Answer 1

Given the following zeros:

-1, 4, 8

Let's determine the polynomial function.

We get,

zeros: -1, 4, 8

It will become,

`\text{ \lparen x + 1\rparen\lparen x - 4\rparen\lparen x - 8\rparen}`

We get,

`\text{ \lparen x + 1\rparen\lparen x - 4\rparen\lparen x - 8\rparen}`
`\text{ \lparen x}^2\text{ - 4x + x - 4\rparen\lparen x - 8\rparen}`
`\text{ \lparen x}^2\text{ - 3x - 4\rparen\lparen x - 8\rparen}`
`\text{ x}^3\text{ - 8x}^2\text{ - 3x}^2\text{ + 24x - 4x + 32}`
`\text{ x}^3\text{ - 11x}^2\text{ + 20x + 32}`

Therefore, the answer is: x³ - 11x² + 20x + 32