GIven:
[tex]P(x)\cdot Q(x)=R(x)[/tex][tex]P(x)=x+2\text{ and }R(x)=x^3-2x^2-6x+4[/tex]Required:
We need to find Q(x).
Explanation:
Consider the equation.
[tex]P(x)\cdot Q(x)=R(x)[/tex][tex]Substitute\text{ }P(x)=x+2\text{ and }R(x)=x^3-2x^2-6x+4\text{ in the equation.}[/tex][tex](x+2)\cdot Q(x)=x^3-2x^2-6x+4[/tex]Divide both sides of the equation by x+2.
[tex]\frac{(x+2)\cdot Q(x)}{x+2}=\frac{x^3-2x^2-6x+4}{x+2}[/tex][tex]Q(x)=\frac{x^3-2x^2-6x+4}{x+2}[/tex]Use long division to divide the given functions.
[tex]Q(x)=\frac{x^3-2x^2-6x+4}{x+2}=x^2-4x+2[/tex][tex]Q(x)=x^2-4x+2[/tex]Final answer:
[tex]Q(x)=x^2-4x+2[/tex]
