Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

### Rational Expressions
#### Polynomial Long Division: Problem Type 1

Divide:
[tex]\[ \left(3x^2 + 9x + 4\right) \div (x + 2) \][/tex]

Provide the quotient and the remainder.

Quotient:
Remainder:

Sagot :

GinnyAnswer
Sure! Let's perform the polynomial long division step-by-step to divide [tex]\(3x^2 + 9x + 4\)[/tex] by [tex]\(x + 2\)[/tex].

1. Setup the Division:
We are dividing [tex]\(3x^2 + 9x + 4\)[/tex] by [tex]\(x + 2\)[/tex].

2. First Division Step:
- Divide the first term of the dividend by the first term of the divisor: [tex]\(\frac{3x^2}{x} = 3x\)[/tex].
- So, the first term of the quotient is [tex]\(3x\)[/tex].

3. First Subtraction Step:
- Multiply [tex]\(3x\)[/tex] by the entire divisor [tex]\(x + 2\)[/tex]: [tex]\(3x \cdot (x + 2) = 3x^2 + 6x\)[/tex].
- Subtract this from the original dividend: [tex]\((3x^2 + 9x + 4) - (3x^2 + 6x)\)[/tex].
- This results in: [tex]\((3x^2 + 9x + 4) - (3x^2 + 6x) = 3x\)[/tex].

4. Second Division Step:
- Divide the first term of the new polynomial by the first term of the divisor: [tex]\(\frac{3x}{x} = 3\)[/tex].
- So, the second term of the quotient is [tex]\(3\)[/tex].

5. Second Subtraction Step:
- Multiply [tex]\(3\)[/tex] by the entire divisor [tex]\(x + 2\)[/tex]: [tex]\(3 \cdot (x + 2) = 3x + 6\)[/tex].
- Subtract this from the new polynomial: [tex]\((3x + 4) - (3x + 6)\)[/tex].
- This results in: [tex]\((3x + 4) - (3x + 6) = -2\)[/tex].

6. Conclusion:
- Now there are no more terms left in the dividend to bring down, and the degree of the remainder [tex]\(-2\)[/tex] is less than the degree of the divisor [tex]\(x + 2\)[/tex].
- Thus, the polynomial long division process is complete.

The quotient is:
[tex]\[ 3x + 3 \][/tex]

And the remainder is:
[tex]\[ -2 \][/tex]

So, the quotient of the division [tex]\( \left(3x^2 + 9x + 4\right) \div (x + 2) \)[/tex] is [tex]\( 3x + 3 \)[/tex] and the remainder is [tex]\( -2 \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.