Question

P(x)⋅Q(x)=R(x) ; if P(x)=x+2 and R(x)=x^3−2x^2−6x+4, what is Q(x)?

Answer 1

GIven:

`P(x)\cdot Q(x)=R(x)`
`P(x)=x+2\text{ and }R(x)=x^3-2x^2-6x+4`

Required:

We need to find Q(x).

Step-by-step explanation:

Consider the equation.

`P(x)\cdot Q(x)=R(x)`
`Substitute\text{ }P(x)=x+2\text{ and }R(x)=x^3-2x^2-6x+4\text{ in the equation.}`
`(x+2)\cdot Q(x)=x^3-2x^2-6x+4`

Divide both sides of the equation by x+2.

`((x+2)\cdot Q(x))/(x+2)=(x^3-2x^2-6x+4)/(x+2)`
`Q(x)=(x^3-2x^2-6x+4)/(x+2)`

Use long division to divide the given functions.

`Q(x)=(x^3-2x^2-6x+4)/(x+2)=x^2-4x+2`
`Q(x)=x^2-4x+2`

Final answer:

`Q(x)=x^2-4x+2`