We appreciate your visit to Divide tex frac x 2 5x 14 x 2 tex Options A tex x 7 tex B tex x 5 tex C tex x 5. 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 division of the polynomial [tex]\((x^2 + 5x - 14)\)[/tex] by [tex]\((x - 2)\)[/tex], we can use polynomial long division. Here's a step-by-step explanation:
1. Set up the division: Divide the polynomial [tex]\(x^2 + 5x - 14\)[/tex] by [tex]\(x - 2\)[/tex].
2. Divide the first term: Divide the first term of the dividend ([tex]\(x^2\)[/tex]) by the first term of the divisor ([tex]\(x\)[/tex]). This gives you [tex]\(x\)[/tex].
3. Multiply and subtract: Multiply the entire divisor [tex]\(x - 2\)[/tex] by [tex]\(x\)[/tex], which gives [tex]\(x^2 - 2x\)[/tex]. Subtract this result from [tex]\(x^2 + 5x - 14\)[/tex]:
[tex]\[
(x^2 + 5x - 14) - (x^2 - 2x) = 7x - 14
\][/tex]
4. Repeat for the next term: Now, divide the first term of the new polynomial [tex]\(7x\)[/tex] by the first term of the divisor [tex]\(x\)[/tex]. This gives you [tex]\(+7\)[/tex].
5. Multiply and subtract again: Multiply the divisor [tex]\(x - 2\)[/tex] by [tex]\(7\)[/tex], resulting in [tex]\(7x - 14\)[/tex]. Subtract this from [tex]\(7x - 14\)[/tex]:
[tex]\[
(7x - 14) - (7x - 14) = 0
\][/tex]
There are no remaining terms; therefore, the remainder is 0.
6. Conclusion: The quotient of the division is [tex]\(x + 7\)[/tex], and since the remainder is 0, [tex]\(x + 7\)[/tex] is the exact result of dividing [tex]\(x^2 + 5x - 14\)[/tex] by [tex]\(x - 2\)[/tex].
So, the solution to the division is [tex]\(x + 7\)[/tex].
1. Set up the division: Divide the polynomial [tex]\(x^2 + 5x - 14\)[/tex] by [tex]\(x - 2\)[/tex].
2. Divide the first term: Divide the first term of the dividend ([tex]\(x^2\)[/tex]) by the first term of the divisor ([tex]\(x\)[/tex]). This gives you [tex]\(x\)[/tex].
3. Multiply and subtract: Multiply the entire divisor [tex]\(x - 2\)[/tex] by [tex]\(x\)[/tex], which gives [tex]\(x^2 - 2x\)[/tex]. Subtract this result from [tex]\(x^2 + 5x - 14\)[/tex]:
[tex]\[
(x^2 + 5x - 14) - (x^2 - 2x) = 7x - 14
\][/tex]
4. Repeat for the next term: Now, divide the first term of the new polynomial [tex]\(7x\)[/tex] by the first term of the divisor [tex]\(x\)[/tex]. This gives you [tex]\(+7\)[/tex].
5. Multiply and subtract again: Multiply the divisor [tex]\(x - 2\)[/tex] by [tex]\(7\)[/tex], resulting in [tex]\(7x - 14\)[/tex]. Subtract this from [tex]\(7x - 14\)[/tex]:
[tex]\[
(7x - 14) - (7x - 14) = 0
\][/tex]
There are no remaining terms; therefore, the remainder is 0.
6. Conclusion: The quotient of the division is [tex]\(x + 7\)[/tex], and since the remainder is 0, [tex]\(x + 7\)[/tex] is the exact result of dividing [tex]\(x^2 + 5x - 14\)[/tex] by [tex]\(x - 2\)[/tex].
So, the solution to the division is [tex]\(x + 7\)[/tex].
Thanks for taking the time to read Divide tex frac x 2 5x 14 x 2 tex Options A tex x 7 tex B tex x 5 tex C tex x 5. 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
