### Home > PC3 > Chapter 10 > Lesson 10.2.2 > Problem10-136

10-136.

Divide each of the following polynomials, $P(x)$, by $D(x)$ to determine the quotient $Q(x)$. Then rewrite the polynomial in the form $P(x) = D(x) · Q(x) + R$, where $R$ is the remainder.

1. $P(x) = 2x^4 − x^2 + 3x + 5 \\D(x) = x − 1$

Notice that there is no $x^{3}$ term. Be sure to include $0x^{3}$ in your division steps.

1. $P(x) = x^5 − 2x^3 + 1 \\D(x) = x − 3$

$\require{enclose} \begin{array}{rll} x^4+3x^3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\[-3pt] x-3 \enclose{longdiv}{x^5+0x^4-2x^3+0x^2+0x+1}\kern-.2ex \\[-3pt] \underline{-(x^5-3x^4)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phantom{00}} && \\[-3pt] 3x^4-2x^3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phantom{0} \\[-3pt] \underline{\phantom{0}-(3x^4-9x^3)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phantom{0}} \\[-3pt] \phantom{0}7x^3+0x^2\ \ \ \ \ \ \ \ \ \ \ \ \ \\[-3pt] \end{array}$