Question

How do you evaluate `f(x)=2x^3+5x^2+4x+8` at x=-2 using direct substitution and synthetic division?

Answer 1

`f(-2)=4`

Explanation:

`f(x)=2x^3+5x^2+4x+8` at `x=-2`

By direct substitution:

`f(-2)=2(-2)^3+5(-2)^2+4(-2)+8`

`f(-2)=2(-8)+5(4)-8+8`

`f(-2)=color(red)4`

By synthetic division:

`-2|2color(white)(aaaa)5color(white)(aaaaa)4color(white)(aaa)8`
`color(white)(a^2aa)darrcolor(white)a-4color(white)(aa)-2color(white)(a)-4`
`color(white)(aaaa)-------`
`color(white)(aaa^22)2color(white)(a^22aa)1color(white)(aaaa^2)2color(white)(aaa)color(red)4`