{"id":17914,"date":"2016-09-24T20:31:40","date_gmt":"2016-09-24T20:31:40","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=17914"},"modified":"2016-09-24T20:31:40","modified_gmt":"2016-09-24T20:31:40","slug":"math-polynomial-long-division","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-polynomial-long-division\/","title":{"rendered":"Math:  polynomial long division"},"content":{"rendered":"<h1>The tutor shows an example of how to divide a polynomial by a binomial.<\/h1>\n<p>Long division with polynomials is appreciated by math teachers, but few others.  What follows is an illustrated example of how to do it.<\/p>\n<p>A simple polynomial long division might begin like this:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div0.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>The process starts with the question, &#8220;How many times does x (from the divisor) go into x<sup>2<\/sup>?&#8221;  The answer is x, and is written on top, above x<sup>2<\/sup>:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div1.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>Next, the x you just wrote on top is multiplied by the divisor; the product is written below the polynomial:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div2.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>Subsequently, subtraction is done, then the next term (in this case, 7) is brought down:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div3.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>Now, the process restarts, with the question, &#8220;How many times does x go into -x (the result of the subtraction)?&#8221;  The answer, -1, is written on top, above the column that contains the -x.  Afterwards, the -1 is multiplied to the divisor, and the result is written below:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div4.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>Subtraction is the next step:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/poly_long_div6.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>The quotient is x-1, the remainder, 5.  If the division is correct,<\/p>\n<p style=\"text-align:center\">(x-1)(x-2) + 5 should equal x<sup>2<\/sup> -3x + 7<\/p>\n<p>Let&#8217;s check:<\/p>\n<p><span style=\"color:#de2133\">(x-1)(x-2)<\/span> + 5 = (using <a href=\"?p=959\">FOIL<\/a>) <span style=\"color:#de2133\">x<sup>2<\/sup> -2x -x + 2<\/span> + 5<\/p>\n<p>Simplifying gives<\/p>\n<p>x<sup>2<\/sup> -3x + 7<\/p>\n<p>Apparently, this long division was successful.<\/p>\n<p>There is yet more to discuss about polynomial long division.  Look for more in coming posts:)<\/p>\n<p>Source:<\/p>\n<p>Travers, Kenneth, et al.  <u>Using Advanced Algebra<\/u>.  Toronto:  Doubleday Canada Limited, 1977.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor shows an example of how to divide a polynomial by a binomial. Long division with polynomials is appreciated by math teachers, but few others. What follows is an illustrated example of how to do it. A simple polynomial &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-polynomial-long-division\/\"> <span class=\"screen-reader-text\">Math:  polynomial long division<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1905,1906,1904],"class_list":["post-17914","post","type-post","status-publish","format-standard","hentry","category-math","tag-how-to-divide-a-polynomial-by-a-binomial","tag-how-to-do-long-division-with-polynomials","tag-polynomial-long-division"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17914","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=17914"}],"version-history":[{"count":38,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17914\/revisions"}],"predecessor-version":[{"id":17952,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17914\/revisions\/17952"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=17914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=17914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=17914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}