Question

Hi, can you help me to Use long division to rewrite ((x) in factored form and find all zeros. Then sketch the graph. Show all work. Please!!

Answer 1

Step 1

Given;

`f(x)=-x^5+7x^4-9x^3-27x^2+54x`

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

`f(x)=-(3)^5+7(3)^4-9(3)^3-27(3)^2+54(3=0`

Hence will divide by a factor of (x-3) and then (x+2)

Step 3

Factorize -x²+3x

`\begin{gathered} -x^2+3x=0 \\ x=0\text{ or 3} \end{gathered}`

Therefore all the zeroes are;

`\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}`