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[2019-01-22 20:13:03] Array
(
[webwork_user] => student1
[problem_set] => Polynomials_-_Division
[problem_number] => 2
[problem_id] => local2/setPolynomial_Division/long-division-nonmonic-linear.pg
[problem_text] => <script type="text/javascript">
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(1 point)
<div class="PGML">
<div style="text-align:center; margin:0">
<h3 style="margin:0">Compute the quotient and the remainder of {{{LATEX_DELIM_INLINE_OPEN}}}\left({-6x^{3}-x^{2}+29x-21}\right) \div \left({2x-3}\right){{{LATEX_DELIM_INLINE_CLOSE}}}</h3>
</div>
<div style="margin-top:1em"></div>
</div>
<div class="section-div"><h3 tabindex=0 id="Prob-2_SC-1_SECT-1" class="iswrong">Long Division: Eliminating the first term</h3><div><script>$("#Prob-2_SC-1_SECT-1").canopen()</script><div class="PGML">
<SECTION style = "display:table;border-collapse:collapse; text-align:center; margin:0 auto; "><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___
</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}2x-3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue; border-left:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}-6 x^3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 1 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 29 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 21{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}\large - ({{{LATEX_DELIM_INLINE_CLOSE}}}___ </DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">___ {{{LATEX_DELIM_INLINE_OPEN}}}\large ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___ </DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV></SECTION></div>
</div></div><div class="section-div"><h3 tabindex=0 id="Prob-2_SC-1_SECT-2" class="iswrong">Long Division: Eliminating the second term</h3><div><script>$("#Prob-2_SC-1_SECT-2").canopen()</script><div class="PGML">
<SECTION style = "display:table;border-collapse:collapse; text-align:center; margin:0 auto; "><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}-3 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___
</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}2x-3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue; border-left:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}-6 x^3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 1 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 29 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 21{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}- ( -6 x^3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 9 x^2 ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}\downarrow{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}-10 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}+29 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}\large - ({{{LATEX_DELIM_INLINE_CLOSE}}}___ </DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">___ {{{LATEX_DELIM_INLINE_OPEN}}}\large ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___ </DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV></SECTION></div>
</div></div><div class="section-div"><h3 tabindex=0 id="Prob-2_SC-1_SECT-3" class="iswrong">Long Division: Eliminating the third term</h3><div><script>$("#Prob-2_SC-1_SECT-3").canopen()</script><div class="PGML">
<SECTION style = "display:table;border-collapse:collapse; text-align:center; margin:0 auto; "><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}-3 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}- 5 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___
</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}2x-3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue; border-left:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}-6 x^3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 1 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 29 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; border-top:2px solid blue;">{{{LATEX_DELIM_INLINE_OPEN}}}- 21{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}- ( -6 x^3{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 9 x^2 ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}\downarrow{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}\downarrow{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}-10 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}+29 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}\downarrow{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}- ( -10 x^2{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}+ 15 x ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}\downarrow{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}14 x{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}- 21{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">{{{LATEX_DELIM_INLINE_OPEN}}}\large - ({{{LATEX_DELIM_INLINE_CLOSE}}}___ </DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; color:red; border-bottom:2px solid black;">___ {{{LATEX_DELIM_INLINE_OPEN}}}\large ){{{LATEX_DELIM_INLINE_CLOSE}}}</DIV></DIV><DIV style = "display:table-row;"><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">{{{LATEX_DELIM_INLINE_OPEN}}}0{{{LATEX_DELIM_INLINE_CLOSE}}}</DIV><DIV style = "display:table-cell;padding:12pt; text-align:center; white-space:nowrap; ">___ </DIV></DIV></SECTION>
<div style="margin-top:1em"></div>
</div>
</div></div><script>
$("#Prob-2_SC-1_SECT-1").opensection();
</script><div class="PGML">
The steps above are provided to help you compute the quotient and remainder.
<div style="margin-top:1em"></div>
If you can find the quotient and remainder without using the steps above, you may input your answer here for full credit:
<div style="margin-top:1em"></div>
The quotient of {{{LATEX_DELIM_INLINE_OPEN}}}\left({-6x^{3}-x^{2}+29x-21}\right) \div \left({2x-3}\right){{{LATEX_DELIM_INLINE_CLOSE}}} is ___
with remainder ___
<div style="margin-top:1em"></div>
</div>
Note: You can earn full credit by answering just the last part.
[course] => WW
[section] => WW-Dev
[remote_course_url] => http://mathww.citytech.cuny.edu/webwork2/WW-Dev/
[remote_problem_url] => http://mathww.citytech.cuny.edu/webwork2/WW-Dev/Polynomials_-_Division/2/
)