Question

How do you use synthetic substitution to evaluate x=4 for `P(x)= x^3 - 4x^2 + 4x - 5`?

Answer 1

`P(4)=11`
(see below for synthetic substitution)

Explanation:

#{: ("line 1:",,,"|",1,-4,+4,-5), ("line 2:",,+,"|",,color(white)("X")4,color(white)("X")0,16), ("line 3:",,"----",,"----","----","----","----"), ("line 4:",,xx(4),"|",1,color(white)("X")0,color(white)("X")4,color(red)(11)) :}#

line 1: the coefficients of the polynomial terms (in descending order of powers of `x`)

line 2: the product of the value of `x` times the value in the previous column of line 4 (see below)

line 3: just a pretty line to keep things in place

line 4: the sum of the the values in this column in lines 1 and 2

The final sum (in line 4) is the value of the polynomial at the required value of `x`