Question

Write a polynomial function in standard form with the given zeros x= -1,-2,-3,-4

Answer 1

Step-by-step explanation: For this question we have 4 zeros so x can be as follows

x = -1 or x = -2 or x = -3 or x = -4

We can turn the equalities above into factors as follows

`\begin{gathered} x=-1\rightarrow x+1=0 \\ x=-2\rightarrow x+2=0 \\ x=-3\rightarrow x+3=0 \\ x=-4\rightarrow x+4=0 \end{gathered}`

Step 1: Now that we have the factors we can build a function and simplify it as follows

`\begin{gathered} y=(x+1)(x+2)(x+3)(x+4) \\ y=(x^2+2x+x+2)(x^2+4x+3x+12) \\ y=(x^2+3x+2)(x^2+7x+12) \\ y=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24 \\ y=x^4+7x^3+3x^3+12x^2+21x^2+2x^2+36x+14x+24 \\ y=x^4+10x^3+35x^2+50x+24 \end{gathered}`

Final answer: So the final answer is

`y=x^4+10x^3+35x^2+50x+24`

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