Solving Polynomial equations by Factoring

Find the product $$\left(x-3\right)\ \left(x^2+\ 3x+9\right)$$  

SAT Question

If y = $$x^3+2x+5\ and\ z=x^2+7x+1,\ what\ is\ 2y+z\ in\ the\ terms\ of\ x?\$$  

Difference of two cubes $$a^{3\ }-\ b^{3\ }=\ \left(a-b\right)\left(a^2+\ ab+b^2\right)\longrightarrow\ \ \ \ \ \ \ \left(x\right)^{3\ }-\ \left(2\right)^3\ =\ \left(x-2\right)\ \left(\ x^2+--\ +\ --\right)$$  

Difference of two cubes $$a^{3\ }-\ b^{3\ }=\ \left(a-b\right)\left(a^2+\ ab+b^2\right)\ \ \ \ \ \ \ \ \ \ x^{3\ }-\ \left(5\right)^3\ =\ \left(x-5\right)\ \left(\ -\ +\ -\ +-\right)$$  

The Sum of two cubes $$x^3+\ y^{3\ }=\ \left(x+y\right)\left(x^{2\ }-\ xy\ +\ y^2\right)$$  

$$\ \ \ \ \ x^3\ +\ \left(3\right)^3$$ =  

The Sum of two cubes $$x^3+\ y^{3\ }=\ \left(x+y\right)\left(x^{2\ }-\ xy\ +\ y^2\right)$$  

$$\ \ \ \ \ x^3\ +\ \left(1\right)^3$$ =

Factor completely $$3\ x^3\ +\ 3\ \left(6\right)^3$$  

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