College

Thank you for visiting Divide using long division frac 3x 5 22x 4 13x 3 39x 2 14x 6 x 3 6x 2 3x 5 Show your work. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Divide using long division.

\[ \frac{-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6}{x^3 + 6x^2 - 3x - 5} \]

(Show your work.)

Answer :

Sure! Let's divide the polynomial [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] by [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex] using long division.

### Step-by-Step Solution:

1. Write the division setup:
[tex]\[
\begin{array}{r|rrrrr}
& -3x^2 & -4x & +2 \\
\hline
x^3 + 6x^2 - 3x - 5 & -3x^5 & -22x^4 & -13x^3 & +39x^2 & +14x & -6 \\
\end{array}
\][/tex]

2. Divide the first terms: [tex]\(-3x^5\)[/tex] (from the dividend) by [tex]\(x^3\)[/tex] (from the divisor), which gives [tex]\(-3x^2\)[/tex].

3. Multiply the entire divisor by [tex]\(-3x^2\)[/tex]:
[tex]\[
\begin{array}{r}
-3x^2(x^3 + 6x^2 - 3x - 5) = -3x^5 - 18x^4 + 9x^3 + 15x^2
\end{array}
\][/tex]

4. Subtract this from the original dividend:
[tex]\[
\begin{array}{rrrrr}
(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6) \\
- (-3x^5 - 18x^4 + 9x^3 + 15x^2) \\
\hline
0 & -4x^4 & -22x^3 & +24x^2 & +14x & -6
\end{array}
\][/tex]

5. Divide the new leading term: [tex]\(-4x^4\)[/tex] by [tex]\(x^3\)[/tex], which gives [tex]\(-4x\)[/tex].

6. Multiply the entire divisor by [tex]\(-4x\)[/tex]:
[tex]\[
\begin{array}{r}
-4x(x^3 + 6x^2 - 3x - 5) = -4x^4 - 24x^3 + 12x^2 + 20x
\end{array}
\][/tex]

7. Subtract this from the current dividend:
[tex]\[
\begin{array}{rrrrr}
(-4x^4 - 22x^3 + 24x^2 + 14x - 6) \\
- (-4x^4 - 24x^3 + 12x^2 + 20x) \\
\hline
0 & 2x^3 & 12x^2 & -6x & -6
\end{array}
\][/tex]

8. Divide the next leading term: [tex]\(2x^3\)[/tex] by [tex]\(x^3\)[/tex], which gives [tex]\(2\)[/tex].

9. Multiply the entire divisor by [tex]\(2\)[/tex]:
[tex]\[
\begin{array}{r}
2(x^3 + 6x^2 - 3x - 5) = 2x^3 + 12x^2 - 6x - 10
\end{array}
\][/tex]

10. Subtract this from the current dividend:
[tex]\[
\begin{array}{rrrr}
(2x^3 + 12x^2 - 6x - 6) \\
- (2x^3 + 12x^2 - 6x - 10) \\
\hline
0 & 0 & 0 & +4
\end{array}
\][/tex]

### Final Result:

After performing these steps, we get the quotient to be:
[tex]\[
-3x^2 - 4x + 2
\][/tex]

And the remainder is:
[tex]\[
4
\][/tex]

So the division of [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] by [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex] is:
[tex]\[
-3x^2 - 4x + 2 + \frac{4}{x^3 + 6x^2 - 3x - 5}
\][/tex]

Thank you for reading the article Divide using long division frac 3x 5 22x 4 13x 3 39x 2 14x 6 x 3 6x 2 3x 5 Show your work. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions