We appreciate your visit to The quotient of tex left x 4 5x 3 3x 15 right tex and tex left x 3 3 right tex is a polynomial What. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the quotient of the polynomial [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex], we can perform polynomial long division. Here's how you can do it step-by-step:
1. Set up the division: Write [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] under the division bar and [tex]\((x^3 - 3)\)[/tex] outside the division bar.
2. Divide the leading terms: Divide the first term of the dividend ([tex]\(x^4\)[/tex]) by the first term of the divisor ([tex]\(x^3\)[/tex]). This gives [tex]\(x\)[/tex]. Write [tex]\(x\)[/tex] as the first term of the quotient.
3. Multiply and subtract: Multiply [tex]\(x\)[/tex] by the entire divisor [tex]\((x^3 - 3)\)[/tex], resulting in [tex]\(x^4 - 3x\)[/tex]. Subtract this result from the original dividend:
[tex]\[
(x^4 + 5x^3 - 3x - 15) - (x^4 - 3x) = 5x^3 - 15
\][/tex]
4. Bring down the next term: Here, we only have [tex]\(5x^3 - 15\)[/tex] left.
5. Repeat the process: Divide the new leading term ([tex]\(5x^3\)[/tex]) by the leading term of the divisor ([tex]\(x^3\)[/tex]), which gives [tex]\(5\)[/tex]. Write [tex]\(5\)[/tex] as the next term of the quotient.
6. Multiply and subtract: Multiply [tex]\(5\)[/tex] by the divisor [tex]\((x^3 - 3)\)[/tex], resulting in [tex]\(5x^3 - 15\)[/tex]. Subtract this from the current expression:
[tex]\[
(5x^3 - 15) - (5x^3 - 15) = 0
\][/tex]
7. Check the remainder: After subtraction, the remainder is [tex]\(0\)[/tex], which means the division is exact.
The final quotient is [tex]\(x + 5\)[/tex].
Hence, the quotient of [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex] is [tex]\(x + 5\)[/tex].
1. Set up the division: Write [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] under the division bar and [tex]\((x^3 - 3)\)[/tex] outside the division bar.
2. Divide the leading terms: Divide the first term of the dividend ([tex]\(x^4\)[/tex]) by the first term of the divisor ([tex]\(x^3\)[/tex]). This gives [tex]\(x\)[/tex]. Write [tex]\(x\)[/tex] as the first term of the quotient.
3. Multiply and subtract: Multiply [tex]\(x\)[/tex] by the entire divisor [tex]\((x^3 - 3)\)[/tex], resulting in [tex]\(x^4 - 3x\)[/tex]. Subtract this result from the original dividend:
[tex]\[
(x^4 + 5x^3 - 3x - 15) - (x^4 - 3x) = 5x^3 - 15
\][/tex]
4. Bring down the next term: Here, we only have [tex]\(5x^3 - 15\)[/tex] left.
5. Repeat the process: Divide the new leading term ([tex]\(5x^3\)[/tex]) by the leading term of the divisor ([tex]\(x^3\)[/tex]), which gives [tex]\(5\)[/tex]. Write [tex]\(5\)[/tex] as the next term of the quotient.
6. Multiply and subtract: Multiply [tex]\(5\)[/tex] by the divisor [tex]\((x^3 - 3)\)[/tex], resulting in [tex]\(5x^3 - 15\)[/tex]. Subtract this from the current expression:
[tex]\[
(5x^3 - 15) - (5x^3 - 15) = 0
\][/tex]
7. Check the remainder: After subtraction, the remainder is [tex]\(0\)[/tex], which means the division is exact.
The final quotient is [tex]\(x + 5\)[/tex].
Hence, the quotient of [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex] is [tex]\(x + 5\)[/tex].
Thanks for taking the time to read The quotient of tex left x 4 5x 3 3x 15 right tex and tex left x 3 3 right tex is a polynomial What. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
