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 solve the problem of finding the quotient of the polynomial [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex], we can use polynomial long division. Here's how you can do it step by step:
1. Set up the division: Write down the dividend [tex]\(x^4 + 5x^3 - 3x - 15\)[/tex] and the divisor [tex]\(x^3 - 3\)[/tex].
2. Divide the leading terms: Divide the leading term of the dividend, [tex]\(x^4\)[/tex], by the leading term of the divisor, [tex]\(x^3\)[/tex]. This gives you the first term of the quotient, which is [tex]\(x\)[/tex].
3. Multiply and subtract: Multiply the entire divisor [tex]\(x^3 - 3\)[/tex] by the first term of the quotient ([tex]\(x\)[/tex]) and subtract the result from the original dividend. This process gets rid of the leading term in the original dividend:
- Multiply: [tex]\(x \cdot (x^3 - 3) = x^4 - 3x\)[/tex].
- Subtract from the original dividend: [tex]\((x^4 + 5x^3 - 3x - 15) - (x^4 - 3x) = 5x^3 + 0x^2 - 15\)[/tex].
4. Repeat the process: Now with the new polynomial [tex]\(5x^3 + 0x^2 - 15\)[/tex], divide the leading term [tex]\(5x^3\)[/tex] by [tex]\(x^3\)[/tex] to get the next term in the quotient, which is [tex]\(+5\)[/tex].
5. Multiply and subtract again: Multiply the entire divisor by this new quotient term ([tex]\(5\)[/tex]) and subtract:
- Multiply: [tex]\(5 \cdot (x^3 - 3) = 5x^3 - 15\)[/tex].
- Subtract from the new polynomial: [tex]\((5x^3 + 0x^2 - 15) - (5x^3 - 15) = 0\)[/tex].
6. End of division: Since the remainder is zero and there are no more terms to drop down, the division is complete. The quotient is [tex]\(x + 5\)[/tex].
The quotient of [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex] is therefore [tex]\(x + 5\)[/tex].
1. Set up the division: Write down the dividend [tex]\(x^4 + 5x^3 - 3x - 15\)[/tex] and the divisor [tex]\(x^3 - 3\)[/tex].
2. Divide the leading terms: Divide the leading term of the dividend, [tex]\(x^4\)[/tex], by the leading term of the divisor, [tex]\(x^3\)[/tex]. This gives you the first term of the quotient, which is [tex]\(x\)[/tex].
3. Multiply and subtract: Multiply the entire divisor [tex]\(x^3 - 3\)[/tex] by the first term of the quotient ([tex]\(x\)[/tex]) and subtract the result from the original dividend. This process gets rid of the leading term in the original dividend:
- Multiply: [tex]\(x \cdot (x^3 - 3) = x^4 - 3x\)[/tex].
- Subtract from the original dividend: [tex]\((x^4 + 5x^3 - 3x - 15) - (x^4 - 3x) = 5x^3 + 0x^2 - 15\)[/tex].
4. Repeat the process: Now with the new polynomial [tex]\(5x^3 + 0x^2 - 15\)[/tex], divide the leading term [tex]\(5x^3\)[/tex] by [tex]\(x^3\)[/tex] to get the next term in the quotient, which is [tex]\(+5\)[/tex].
5. Multiply and subtract again: Multiply the entire divisor by this new quotient term ([tex]\(5\)[/tex]) and subtract:
- Multiply: [tex]\(5 \cdot (x^3 - 3) = 5x^3 - 15\)[/tex].
- Subtract from the new polynomial: [tex]\((5x^3 + 0x^2 - 15) - (5x^3 - 15) = 0\)[/tex].
6. End of division: Since the remainder is zero and there are no more terms to drop down, the division is complete. The quotient is [tex]\(x + 5\)[/tex].
The quotient of [tex]\((x^4 + 5x^3 - 3x - 15)\)[/tex] divided by [tex]\((x^3 - 3)\)[/tex] is therefore [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
