Question

Question #e9a58

Answer 1

`color(blue)(x^3+2x^2+3x+6`

Explanation:

`(x+1)(x^2+3)`

`color(white)(aaaaaaaaaaaaa)` `x^2+3`
`color(white)(aaaaaaaaaaaaaa)` `x+1`
`color(white)(aaaaaaaaaaaaa)` `-----`
`color(white)(aaaaaaaaaaaaaa)` `x^3` `color(white)(aaaa)` `+3x`
`color(white)(aaaaaaaaaaaaaaaaa)` `2x^2` `color(white)(aaaa)` `+6`
`color(white)(aaaaaaaaaaaaa)` `------`
`color(white)(aaaaaaaaaaaa)` `color(blue)(x^3+2x^2+3x+6`

Answer 2

`3x^2+4x+3`

Explanation:

`"Expand the brackets"`

`(x+2)(x^2+3)=x^3+2x^2+3x+6`

differentiate each term using the `color(blue)"power rule"`

`• d/dx(ax^n)=nax^(n-1)`

`rArrd/dx(x^3+2x^2+3x+6)`

`=3x^2+4x+3`