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

Graph the polynomial function, factor first if the expression is not in factored form-example-1

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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;

Graph the polynomial function, factor first if the expression is not in factored form-example-1
User Artfulhacker
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