Question

Graph the polynomial function, factor first if the expression is not in factored form.

Answer 1

Given the function;

`f(x)=x^3+10x^2+17x-28`

we are asked to factor and then graph the function. This can be seen below.

Step-by-step explanation

`f(x)=x^2+10x^2+17x-8`

To factorize the function f(x) we will use the rational root theorem to factorize the above;

`Possible\text{ Rational Roots =}\frac{factors\text{ of the constant}}{factors\text{ of the lead coefficient}}`

Hence;

`\begin{gathered} Possible\text{ Rational Roots =}(\pm1,\pm2,\pm4\pm7,\pm14,\pm28)/(\pm1) \\ Possible\text{ rational roots =}\pm1,\pm2,\pm4,\pm7,\pm14,\pm28 \end{gathered}`

When we test the rational roots in the given function, the only suitable ones are;

`+1,-4,-7`

The factors can be expressed as;

`\begin{gathered} factor\text{ =\lparen x-a\rparen} \\ where\text{ a is the root} \end{gathered}`

Therefore; the factors become

`f(x)=(x-1)(x+4)(x+7)`

Hence, the plot of the graph becomes;