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Relationship Between Solutions to an Equation and Zeroes of a Function

Solve the equation $\mathbf{x^4+x^3-7x^2-x+6=0}$ given that (x-2) and (x+3) are factors. Graph the equation.

To solve: 1.) Long division 2.) synthetic division

factor:(x-2) x-2=0 x=2
factor: (x+3) x+3=0 x-3
Guess: (x+1) x+1=0 x=-1 (x-2)(x+3)(x+1)(x-1)=0 Factored Form
degree: 4 leading coefficient: 1 $x \rightarrow \infty \quad \quad f(x) \rightarrow \infty$ $x \rightarrow -\infty \quad \quad f(x) \rightarrow \infty^-$