Step 1
Given;
[tex]f(x)=-x^5+7x^4-9x^3-27x^2+54x[/tex]
Required; To Use long division to rewrite ((x) in factored form and find all zeros.
Then sketch the graph.
Step 2
Rewrite ((x) in factored form. one of the zeroes of f(x) is x=3
[tex]f(x)=-(3)^5+7(3)^4-9(3)^3-27(3)^2+54(3=0[/tex]
Hence will divide by a factor of (x-3) and then (x+2)
Step 3
Factorize -x²+3x
[tex]\begin{gathered} -x^2+3x=0 \\ x=0\text{ or 3} \end{gathered}[/tex]
Therefore all the zeroes are;
[tex]\begin{gathered} x=\text{ 3 thrice, -2 and 0} \\ \text{That is x has a zero which is 3 with a multiplicity of 3} \\ \text{x has a zero which is 0 with a multiplicity of }1 \\ \text{x has a zero which is -2 with a multiplicity of }1 \end{gathered}[/tex]
