How to Perform Synthetic Division Definition, Types, Examples & Uses

How to Perform Synthetic Division

Subject: Mathematics

Book: Maths Mastery

Synthetic division streamlines dividing polynomials by linear factors of the form (x – c). For instance, to divide x³–2x²+4x–8 by (x–2), set up synthetic placeholders using 2 as the “root” and coefficients 1, –2, 4, –8. Bring down the leading coefficient and multiply it by 2 each time, adding to the next column. The final row’s last number is the remainder; preceding numbers are new coefficients. This method cuts out the repeated steps of polynomial long division. Widely used in factorization and root finding, synthetic division is a quick and powerful algebraic technique for linear divisors.