Question

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Answer 1

From the problem, we have the zeros -1, multiplicity 2. This will be (x + 1)^2

4 multiplicity 1, this will be (x - 4)

The function will be :

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

Simplify by expanding the binomial :

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

Distribute and multiply (x - 4) to the trinomial :

`\begin{gathered} f(x)=x(x^2+2x+1)-4(x^2+2x+1) \\ f(x)=(x^3+2x^2+x)-(4x^2+8x+4) \\ f(x)=x^3+2x^2+x-4x^2-8x-4 \\ f(x)=x^3-2x^2-7x-4 \end{gathered}`

The answer is C.