Question

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

Answer 1

`f(-2)=color(green)(62)`

Explanation:

`{: (,color(white)("XXX"),,x^4,x^3,x^2,x^1,x^0), ("row 1:",,"|",1,-4,0,-4,6), ("row 2:",underline(color(white)("XXX")),"|",underline(color(white)("XX")),underline(-2),underline(12),underline(-24),underline(+56)), ("row 3:",-2,"|",1,-6,12,-28,color(red)62) :}`

Values in row 3 are formed from the sum of the values in rows 1 and 2 of that column.

Values in row 2 are formed from the product of the argument value (in this case `(-2)` and the value in row 3 of the previous column.

The final value in row 3 is the value of the function at the argument value.