How do you use synthetic substitution to evaluate ##P(x) = 4x^2 - 9x + 2## for ##x=3##?

Answer is 11, You use the L shaped box (read below)

So first step is to create that L shaped box and write 3 outside of it.

The first number is the coefficient of the greatest power, or 4, since it's with ##x^2##. Go in order, the next number should be the coefficient of x, and the next after that is ##x^0=1##.

Pull the first number down without doing anything to it, then multiply that by the number outside the L so ##4 * 3 = 12## take that answer and put it back in under the second coefficient and add them together -9 + 12 = 3

then take that answer, multiply by the number outside the box ##3 * 3 = 9## and put that under the third coefficient and add them together 2+9=11

Plug x=3 into the equation to check.