Explanation:
The polynomial is given below as
[tex]f(x)=x^4+2x^3-7x^2-8x+12[/tex]
Given in the question above the real zeros are gotten below as
[tex]x=-3,-2,1,2[/tex]
Concept:
To figure out the factor form of the polynoimial, we will equate each zero to x below as
[tex]\begin{gathered} x=c \\ (x-c) \end{gathered}[/tex]
Therefore,
The factored form of the polynomial will be
[tex]\begin{gathered} f(x)=x^{4}+2x^{3}-7x^{2}-8x+12 \\ x=-3,x=-2,x=1,x=2 \\ f(x)=(x+3)(x+2)(x-1)(x-2) \end{gathered}[/tex]
Hence,
Using the real zeros of f(x) , the factored form of the polynomial is
[tex]\Rightarrow f(x)=(x+3)(x+2)(x-1)(x-2)[/tex]
