SOURCE

$("#add").click(function() {
  var p1 = extractPoly($("#p1").val());
  var p2 = extractPoly($("#p2").val());
  var sum = p1.add(p2);
  $("#result").html(sum.toString());
});

$("#mult").click(function() {
  var p1 = extractPoly($("#p1").val());
  var p2 = extractPoly($("#p2").val());
  var sum = p1.mult(p2);
  $("#result").html(sum.toString());
});

function extractPoly(input) {
  var l = input.replace(/\-/g, "\+-").split("+");
  parms = [];
  var cf;
  l.forEach(function(x, y, z) {
    t = x.split('^');
    if (t[0] && t[0].indexOf('x') < 0) {
      parms.push({
        "cof": parseFloat(t[0]),
        "exp": 0
      });
    } else if (t[0] && t[0].indexOf('x') >= 0) {
      cf = t[0].replace('x', '');
      cf = isNaN(parseFloat(cf)) ? parseFloat(cf + '1') : parseFloat(cf);
      parms.push({
        "cof": cf,
        "exp": t[1] ? parseFloat(t[1]) : 1
      });
    }
  });
  parms.sort(function(a, b) {
    return a.exp - b.exp;
  });
  var cofs = [];
  var exps = [];
  parms.forEach(function(x, y, z) {
    cofs.push(x.cof);
    exps.push(x.exp);
  });
  console.log(parms, cofs, exps);
  var p = new Poly(cofs, exps);
  return p;
}

<div class="container">
  <div class="panel panel-default">
    <div class="panel-heading">简易多项式运算</div>
    <div class="panel-body">
      <div class="poly">
        <label for='p1'>p1 =</label>
        <textarea id="p1" class="form-control" style="max-width:100%" rows="1" placeholder="Input a polynomial like:-1+x-x^2+x^5">-1+x-2x^3</textarea>
      </div>
      <div class="poly">
        <label for='p2'>p2 =</label>
        <textarea id="p2" class="form-control" style="max-width:100%" rows="1" placeholder="Input a polynomial like:-1+x-x^2+x^5">1+x^2</textarea>
      </div>
      <div class="btn-group">
        <button class="btn btn-default btn-sm" id="add">+

        </button>
        <button class="btn btn-default btn-sm" id="mult">×</span>

        </button>
      </div>
      <div class="output" style="margin=5">
        <label>=</label>
        <div class="well" id="result"></div>
      </div>
    </div>
    <div class="panel-footer">
      <div id="author">Author: <a href="http://wuzhiwei.net/about/" target="_blank">Tim Wu</a>

      </div>
    </div>
  </div>
</div>

textarea.form-control {
  margin-bottom: 7px;
}

.panel-heading {
  text-align: center;
}

#author {
  text-align: right;
}