Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To divide the polynomial [tex]\(12x^5 - 36x^4 - 6x^3\)[/tex] by [tex]\(3x^2\)[/tex], you can follow these steps:
1. Divide each term of the numerator by the divisor: [tex]\(3x^2\)[/tex].
Let's break it down term by term:
- The first term is [tex]\(12x^5\)[/tex]:
[tex]\[ \frac{12x^5}{3x^2} = 4x^{5-2} = 4x^3 \][/tex]
- The second term is [tex]\(-36x^4\)[/tex]:
[tex]\[ \frac{-36x^4}{3x^2} = -12x^{4-2} = -12x^2 \][/tex]
- The third term is [tex]\(-6x^3\)[/tex]:
[tex]\[ \frac{-6x^3}{3x^2} = -2x^{3-2} = -2x \][/tex]
2. Combine the simplified terms:
Therefore, the result of the division is:
[tex]\[ \frac{12x^5 - 36x^4 - 6x^3}{3x^2} = 4x^3 - 12x^2 - 2x \][/tex]
So, the correct answer is:
[tex]\[ 4x^3 - 12x^2 - 2x \][/tex]
This matches the option:
[tex]\[ \boxed{4x^3 - 12x^2 - 2x} \][/tex]
1. Divide each term of the numerator by the divisor: [tex]\(3x^2\)[/tex].
Let's break it down term by term:
- The first term is [tex]\(12x^5\)[/tex]:
[tex]\[ \frac{12x^5}{3x^2} = 4x^{5-2} = 4x^3 \][/tex]
- The second term is [tex]\(-36x^4\)[/tex]:
[tex]\[ \frac{-36x^4}{3x^2} = -12x^{4-2} = -12x^2 \][/tex]
- The third term is [tex]\(-6x^3\)[/tex]:
[tex]\[ \frac{-6x^3}{3x^2} = -2x^{3-2} = -2x \][/tex]
2. Combine the simplified terms:
Therefore, the result of the division is:
[tex]\[ \frac{12x^5 - 36x^4 - 6x^3}{3x^2} = 4x^3 - 12x^2 - 2x \][/tex]
So, the correct answer is:
[tex]\[ 4x^3 - 12x^2 - 2x \][/tex]
This matches the option:
[tex]\[ \boxed{4x^3 - 12x^2 - 2x} \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.