Using Synthetic Division to FactorA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series
Using Synthetic Division to Factor One way that we can factor a polynomial is to use synthetic division. Synthetic division factoring can be an effective way to factor complicated polynomials with whole number coefficients. When factoring using synthetic division, we determine one of the roots and use synthetic division to determine the remaining coefficient. If the remaining coefficient is equal to zero, then the expression is divisible by that factor.
Solving by Factoring The first step is to bring all the terms to one side and set the equation equal to zero. Next, using the method of solving by factoring, take out the common terms and use one of the methods of factoring to simplify the expression. Once in this multiplication form, note that if two terms multiplied equal zero, one of the terms must be equal to zero. Given the rational roots theorem, these are the solutions to the equation.
Rational Roots Theorem The rational roots theorem states that all potential roots are in the positive or negative form of the last coefficient’s factors divided by the first coefficient’s factors. With a large polynomial, solving by factoring is more difficult, and so finding the rational roots will give some potential zeros to start with. With these rational roots, the solutions after factoring complicated expressions is narrowed down to a select few answers.
Using Synthetic Division to Solve an Equation: Synthetic Division Polynomials To solve a polynomial equation using synthetic division, we first use the rational roots theorem to determine the potential zeroes for factoring. After factoring, we can solve synthetic division polynomials by setting each of our factors equal to the other side of the equation and solving.
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