Question

What would be the first and last terms of the polynomial if it was written in standard form? (x-2)^5 ÷ (x-2)

Answer 1

In standard form the equation will be
`x^4-4x^3+12x^2-16x+16`

Explanation:

We have given polynomial
`((x-2)^5)/((x-2))`

After dividing the expression will be
`(x-2)^4`

`(x-2)^4` can be written as
`(x-2)^2* (x-2)^2`

`(x-2)^2* (x-2)^2=(x^2+4-4x)(x^2+4-4x)=x^4+4x^2-2x^3+4x^2+16-8x-2x^3-8x+4x^2=x^4-4x^3+12x^2-16x+16`

So in standard form the equation will be
`x^4-4x^3+12x^2-16x+16`