In this section we learn about synthetic division of polynomials. This will provide us with a quick method for dividing polynomials by linear functions using the nested scheme, a.k.a Horner's Method.
For instance, by the end of this section we'll know how to quickly find the quotient and remainder functions for the following division: \[\begin{pmatrix} 3x^5 - 2x^3 + x^2 - 3x + 10\end{pmatrix} \div \begin{pmatrix} x - 2 \end{pmatrix} \]
These two introductory examples show the different scenarious we learn here:
In this first tutorial we see two examples. We divide divide \(f(x) = x^5 + 2x^3 - 3x^2 - 4x + 5\) by \(g(x) = x-2\) as well as \(f(x) = 4x^4 - 2x^3 + 7x + 10\) by \(g(x) = x+1\).
In this second tutorial we learn how to divide a polynomial by a linear function whose \(x\) coefficient isn't equal to \(1\). In particular we divide \(f(x) = 2x^4 - 4x^2 - 6x - 5\) by \(g(x) = 2x - 6\).
For each of the following, use syntehtic division to find \(f(x) \div g(x)\). In each case, specify the quotient polynomial function, \(Q(x)\), as well as the remainder \(R\).
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