Given the function;
[tex]f(x)=x^3+10x^2+17x-28[/tex]
we are asked to factor and then graph the function. This can be seen below.
Explanation
[tex]f(x)=x^2+10x^2+17x-8[/tex]
To factorize the function f(x) we will use the rational root theorem to factorize the above;
[tex]Possible\text{ Rational Roots =}\frac{factors\text{ of the constant}}{factors\text{ of the lead coefficient}}[/tex]
Hence;
[tex]\begin{gathered} Possible\text{ Rational Roots =}\frac{\pm1,\pm2,\pm4\pm7,\pm14,\pm28}{\pm1} \\ Possible\text{ rational roots =}\pm1,\pm2,\pm4,\pm7,\pm14,\pm28 \end{gathered}[/tex]
When we test the rational roots in the given function, the only suitable ones are;
[tex]+1,-4,-7[/tex]
The factors can be expressed as;
[tex]\begin{gathered} factor\text{ =\lparen x-a\rparen} \\ where\text{ a is the root} \end{gathered}[/tex]
Therefore; the factors become
[tex]f(x)=(x-1)(x+4)(x+7)[/tex]
Hence, the plot of the graph becomes;
