Print preview
Worksheet Polynomial Long Division
2.
3.
4.
5.
6.
7.
Use synthetic division to determine whether or not \((x-5)\) is a factor of \(({-5x^{3}+30x^{2}-28x+15})\text{.}\)
-
Quotient:
-
Remainder:
8.
Use synthetic division to determine whether or not \((x-5)\) is a factor of \(({-3x^{3}+17x^{2}-9x-5})\text{.}\)
-
Quotient:
-
Remainder:
9.
10.
11.
Use long division to divide \(({2x^{2}+7x+5})\div(x-8)\text{.}\) Find the quotient and remainder.
Hint.
The initial setup should look like this:
with the divisor to the left and the dividend to the right.
The first step is to eliminate the first term of the dividend. To do this, divide the highest term of \({2x^{2}+7x+5}\) by the highest term of \(x-8\text{.}\) The result is the highest term of the quotient.
The set up at the end of the next step should look like:
Now you should repeat the process again to identify the quotient and remainder.
12.
Divide the quartic polynomial \(f(x) = x^{4}-3x^{3}-13x^{2}+12x+12\) by the linear polynomial \(g(x) = x-5\text{.}\)
(a) Determine the quotient
-
\(\displaystyle x^{3}+2x^{2}+5x+3\)
-
\(\displaystyle x^{3}+2x^{2}-3x-3\)
-
\(\displaystyle x^{3}+3x^{2}-4x+3\)
-
\(\displaystyle x^{3}+x^{2}-2x+1\)
(b) Determine the remainder.
(c) Evaluate \(f(5)\text{.}\)
13.
Use long division to find the quotient and remainder when
\begin{equation*}
f(x)=-8 x^5 - 4 x^4 + 4 x^3 + 6 x^2 + 7 x - 5
\end{equation*}
is divided by
\begin{equation*}
g(x)=4 x^2 + 8 x + 5.
\end{equation*}
The quotient is .
The remainder is .
