Division by Polynomials

$\blacktriangleright$ To convert a quotient of polynomials ${\dfrac{{f(x)}}{{% g(x)}}}$ with rational coefficients to the form q(x) + ${\dfrac{{r(x)}}{{g(x)}}}$, where r(x) and q(x) are polynomials and deg r(x) < deg g(x)

1.
Enter a quotient of polynomials.

2.
Leave the insertion point in the expression.

3.
From the Polynomials submenu, choose Divide .

$\blacktriangleright$ Polynomials + Divide

$\left(\vphantom{ 3x^{2}+3x}\right.$3x2 + 3x$\left.\vphantom{ 3x^{2}+3x}\right)$/$\left(\vphantom{ 8x^{2}+7}\right.$8x2 + 7$\left.\vphantom{ 8x^{2}+7}\right)$ = ${\dfrac{{3}}{{8}}}$ + ${\dfrac{{3x-\frac{21}{8}}}{{8x^{2}+7}}}$

${\dfrac{{3x^{5}+3x^{3}-4x^{2}+5}}{{8x^{2}+7}}}$ = ${\dfrac{{3}}{{8}}}$x3 + ${\dfrac{{3}}{{64}}}$x - ${\dfrac{{1}}{{2}}}$ + ${\dfrac{{\frac{17}{2}-\frac{21}{64}x}}{{8x^{2}+7}}}$


${\dfrac{{128x^{6}+128x^{5}+128x^{4}+768x^{3}-128x^{2}+\allowbreak 128x-128}}{{% 16x^{4}+8x^{3}+70x^{2}+7x+49}}}$ = 8x2 +4x - 29 + ${\dfrac{{% 664x^{3}+1482x^{2}+135x+1293}}{{16x^{4}+8x^{3}+70x^{2}+7x+49}}}$

Note    This algorithm is the familiar long division algorithm for polynomials.