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

##### 1 Answer
Oct 24, 2015

If $f \left(x\right) = {x}^{4} - 4 {x}^{3} - 4 x + 6$ then $f \left(- 3\right) = 207$

#### Explanation:

In performing synthetic substitution:
$\textcolor{w h i t e}{\text{XXX}}$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 $0$
$\textcolor{w h i t e}{\text{XXX}}$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.