Thank you for visiting Divide using long division tex frac 3x 5 22x 4 13x 3 39x 2 14x 6 x 3 6x 2 3x 5 tex SHOW 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!
Answer :
Sure, let's solve the given problem step-by-step using long division.
We need to divide the polynomial [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] by the polynomial [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex].
### Step 1: Set up the division
The dividend is [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] and the divisor is [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex].
We'll write it in the long division format:
```
________________
x^3 + 6x^2 - 3x - 5 | -3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6
```
### Step 2: Divide the leading terms
First, we divide the leading term of the dividend by the leading term of the divisor:
[tex]\[
\frac{ -3x^5 }{ x^3 } = -3x^2
\][/tex]
### Step 3: Multiply and subtract
Now, we multiply [tex]\( -3x^2 \)[/tex] by the entire divisor:
[tex]\[
-3x^2 \cdot (x^3 + 6x^2 - 3x - 5) = -3x^5 - 18x^4 + 9x^3 + 15x^2
\][/tex]
We subtract this from the dividend:
[tex]\[
\begin{align*}
(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6) \\
- (-3x^5 - 18x^4 + 9x^3 + 15x^2) \\
= 0x^5 - 4x^4 - 22x^3 + 24x^2 + 14x - 6
\end{align*}
\][/tex]
### Step 4: Repeat the process
Next, we divide the new leading term by the leading term of the divisor:
[tex]\[
\frac{-4x^4 }{ x^3 } = -4x
\][/tex]
Multiply and subtract:
[tex]\[
\begin{align*}
-4x \cdot (x^3 + 6x^2 - 3x - 5) = -4x^4 - 24x^3 + 12x^2 + 20x \\
0x^5 - 4x^4 - 22x^3 + 24x^2 + 14x - 6 \\
- ( -4x^4 - 24x^3 + 12x^2 + 20x) \\
= 0x^4 + 2x^3 + 12x^2 - 6x - 6
\end{align*}
\][/tex]
### Step 5: Continue the process
Next, we divide:
[tex]\[
\frac{2x^3}{x^3} = 2
\][/tex]
Multiply and subtract:
[tex]\[
\begin{align*}
2 \cdot (x^3 + 6x^2 - 3x - 5) = 2x^3 + 12x^2 - 6x - 10 \\
0x^4 + 2x^3 + 12x^2 - 6x - 6 \\
- ( 2x^3 + 12x^2 - 6x - 10) \\
= 0x^3 + 0x^2 + 0x + 4
\end{align*}
\][/tex]
### Step 6: Write the final quotient and remainder
The division process is complete, and the quotient is:
[tex]\[
-3x^2 - 4x + 2
\][/tex]
And the remainder is:
[tex]\[
4
\][/tex]
Therefore, the final answer is:
[tex]\[
-3x^2 - 4x + 2 \quad \text{with a remainder of} \quad 4
\][/tex]
So, [tex]\(\frac{-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6}{x^3 + 6x^2 - 3x - 5} = -3x^2 - 4x + 2 + \frac{4}{x^3 + 6x^2 - 3x - 5}\)[/tex].
We need to divide the polynomial [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] by the polynomial [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex].
### Step 1: Set up the division
The dividend is [tex]\(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6\)[/tex] and the divisor is [tex]\(x^3 + 6x^2 - 3x - 5\)[/tex].
We'll write it in the long division format:
```
________________
x^3 + 6x^2 - 3x - 5 | -3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6
```
### Step 2: Divide the leading terms
First, we divide the leading term of the dividend by the leading term of the divisor:
[tex]\[
\frac{ -3x^5 }{ x^3 } = -3x^2
\][/tex]
### Step 3: Multiply and subtract
Now, we multiply [tex]\( -3x^2 \)[/tex] by the entire divisor:
[tex]\[
-3x^2 \cdot (x^3 + 6x^2 - 3x - 5) = -3x^5 - 18x^4 + 9x^3 + 15x^2
\][/tex]
We subtract this from the dividend:
[tex]\[
\begin{align*}
(-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6) \\
- (-3x^5 - 18x^4 + 9x^3 + 15x^2) \\
= 0x^5 - 4x^4 - 22x^3 + 24x^2 + 14x - 6
\end{align*}
\][/tex]
### Step 4: Repeat the process
Next, we divide the new leading term by the leading term of the divisor:
[tex]\[
\frac{-4x^4 }{ x^3 } = -4x
\][/tex]
Multiply and subtract:
[tex]\[
\begin{align*}
-4x \cdot (x^3 + 6x^2 - 3x - 5) = -4x^4 - 24x^3 + 12x^2 + 20x \\
0x^5 - 4x^4 - 22x^3 + 24x^2 + 14x - 6 \\
- ( -4x^4 - 24x^3 + 12x^2 + 20x) \\
= 0x^4 + 2x^3 + 12x^2 - 6x - 6
\end{align*}
\][/tex]
### Step 5: Continue the process
Next, we divide:
[tex]\[
\frac{2x^3}{x^3} = 2
\][/tex]
Multiply and subtract:
[tex]\[
\begin{align*}
2 \cdot (x^3 + 6x^2 - 3x - 5) = 2x^3 + 12x^2 - 6x - 10 \\
0x^4 + 2x^3 + 12x^2 - 6x - 6 \\
- ( 2x^3 + 12x^2 - 6x - 10) \\
= 0x^3 + 0x^2 + 0x + 4
\end{align*}
\][/tex]
### Step 6: Write the final quotient and remainder
The division process is complete, and the quotient is:
[tex]\[
-3x^2 - 4x + 2
\][/tex]
And the remainder is:
[tex]\[
4
\][/tex]
Therefore, the final answer is:
[tex]\[
-3x^2 - 4x + 2 \quad \text{with a remainder of} \quad 4
\][/tex]
So, [tex]\(\frac{-3x^5 - 22x^4 - 13x^3 + 39x^2 + 14x - 6}{x^3 + 6x^2 - 3x - 5} = -3x^2 - 4x + 2 + \frac{4}{x^3 + 6x^2 - 3x - 5}\)[/tex].
Thank you for reading the article Divide using long division tex frac 3x 5 22x 4 13x 3 39x 2 14x 6 x 3 6x 2 3x 5 tex SHOW 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!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
