Question

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

Answer 1

at `x=2`, `3x^5-2x^2+x=color(green)(90)`
(see below for methods of evaluation)

Explanation:

By direct substitution
At `x=2`
`color(white)("XXX"){: (3x^5,=,3xx32=,96), (-2x^2,=,,-8), (x,=,,underline(2)), (,,,color(green)(90)) :}`

By synthetic division

`{: (,,x^5,x^4,x^3,x^2,x^1,x^0), (," | ",3,+0,+0,-2,+1,+0), (underline(color(white)("XXX")),underline(" | "),underline(color(white)("XX")),underline(6),underline(12),underline(24),underline(44),underline(90)), (2xx," | ",3,6,12,22,45,color(green)(90)) :}`