Question

5. What is a cubic polynomial function in standard form with zeros 1, –2, and 2? (1 point)

= x3 + x2 – 3x + 4
= x3 + x2 – 4x – 2
= x3 + x2 + 4x + 4
= x3 – x2 – 4x + 4

Answer 1

Hello,

Answer D
(x-1)(x+2)(x-2)=(x-1)(x²-4)=x^3-x²-4x+4

Answer 2

Option D is correct

The cubic polynomial function in standard form is :

`x^3-x^2-4x+4`

Explanation:

Given the zeroes of the polynomial function 1 , -2 and 2.

i.e, x = 1 , -2 and 2 where x is the zero of the polynomial function.

we can write this as

x - 1 = 0,

x + 2 = 0 or

x - 2 = 0

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

Using identities
`(a+b)(a-b) =a^2-b^2`

then;

`(x-1)(x^2-4)=0`

Multiply the first term of the first expression with second expression;

`x (x^2-4) =x^3-4x`

also,

Multiply the second term of the first expression with second expression;

`1(x^2-4) = x^2 -4`

Now, subtract
`x^3-4x` and
`x^2 -4`

we get;

`x^3-4x-x^2+4`

then, we have;

`x^3-x^2-4x+4=0`

Cubic function is any function of the form
`y = ax^3 + bx^2 + cx + d,` where a, b, c, and d are constants and a≠0

therefore, the given function is cubic function;

so, the cubic function f(x) =
`x^3-x^2-4x+4`