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Synthetic division can only be used if you re dividing by a linear factor in the form x a.
Synthetic long math. Synthetic division is a shorthand or shortcut method of polynomial division in the special case of dividing by a linear factor and it only works in this case. It won t work for every math topic but it s super helpful for topics when several methods can be used. We can simplify the division by detaching the coefficients. What is synthetic division.
Polynomial synthetic division is a simplified form of polynomial division that is used only in the case of division by a linear factor a monomial. Synthetic division is an abbreviated way of dividing a polynomial by a binomial of the form x c or x c. Most high school algebra textbooks cover two methods for dividing polynomials. It all started with dividing polynomials using synthetic and long division.
It is most commonly used to find roots of a polynomial. Long division and synthetic division. Synthetic division is a method similar to polynomial long division but it requires less writing and fewer calculations however it can be used only for dividing polynomial in one variable by linear polynomial x a. It does away with division brackets and variables used in polynomial long division and focuses on the coefficients of the polynomial in question.
If you need to divide by a polynomial with a higher degree or one that doesn t have a 1 as the leading coefficient you ll have to do plain old long division. Math worksheets in this lesson we will look at synthetic division which is simplified form of long division. Every year my students loathed long division and it showed on assessments.
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