Question

How do you use synthetic substitution to find f(-2) for `f(x) = x^4 - 4x^3 - 4x + 6`?

Answer 1

If `f(x)=x^4-4x^3-4x+6` then `f(-3) = 207`

Explanation:

In performing synthetic substitution:
`color(white)("XXX")`the top row of numbers are coefficients of the terms of the dividend arranged in descending degree (be sure to include terms with coefficients of `0`
`color(white)("XXX")`the number on the left at the bottom is the evaluation value (the value for which the polynomial is being evaluated.

For each column, the top 2 numbers are added to give a third number in that column.
The third number in that column is multiplied by the evaluation value and the product is written as the second number in the next column.

`{: (,,x^4,x^3,x^2,x^1,x^0), (,"|",1,-4,+0,-4,+6), ("Add","|",,-3,21,-63,201), (xx(-3),"|",1,-7,21,-67,color(red)(207)) :}`

When the last column has bee processed, the last sum (the third number in the last column) is the value of the polynomial at the evaluation value.