Synthetic multiplication is a method of multiplying polynomials by considering only the coefficients. The coefficients can be considered as forming ordinary numbers and multiplied in the normal way, with the result of the multiplication being translated back into a polynomial.
Consider the product
Expanding the brackets gives, after some simplification,
Now write the polynomial
as 213 and the polynomial
as 122,
213*122=25986.
2, 5, 9, 8 and 6 are the coefficients of
and 6 is the constant term respective,ly so we can write down the result of multiplying the two polynomials as
Synthetic multiplication is limited and cannot handle carried digits so that we would not be abke to multiply
by
In fact
Using synthetic multiplication, writingas 47 and
as 36, we obtain 47*36=1692, which would give the polynomial
which is obviously wrong.