Problem 52861. Easy Sequences 37: Natural Factorable Polynomials

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A polynomial of the form: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^n+a_2x^{n-1}+a_3x^{n-2}+...+a_{n-2}x^2+a_{n-1}x+a_n</w:t></w:r></w:customXml><w:r><w:t>, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n &gt; 1</w:t></w:r></w:customXml><w:r><w:t>, is said to be natural factorable if it can be factored into products of first degree binomials: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>(x+r_1)(x+r_2)...(x+r_{n-1})(x+r_n)</w:t></w:r></w:customXml><w:r><w:t>, where, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a_2,\\ a_3,\\ a_4,\\ ...\\ a_{n-1},\\ a_n</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r_1,\\ r_2,\\ r_3,\\ ...\\ r_{n-1},\\ r_n</w:t></w:r></w:customXml><w:r><w:t> are </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>all</w:t></w:r><w:r><w:t> natural numbers (i.e. integers that are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\ge1</w:t></w:r></w:customXml><w:r><w:t>).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1 &lt; a_2\\le a</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, when </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a = 4</w:t></w:r></w:customXml><w:r><w:t>, the are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>7</w:t></w:r></w:customXml><w:r><w:t> possible natural factorable polynomials, namely:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^2+2x+1=(x+1)^2</w:t></w:r></w:customXml><w:r><w:t>;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^2+3x+2=(x+1)(x+2)</w:t></w:r></w:customXml><w:r><w:t>;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^2+4x+3 = (x+1)(x+3)</w:t></w:r></w:customXml><w:r><w:t>;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^2+4x+4 = (x+2)^2</w:t></w:r></w:customXml><w:r><w:t>;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>x^3+3x^2+3x+1=(x+1)^3</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x^3+4x^2+5x+2 = (x+1)^2(x+2)</w:t></w:r></w:customXml><w:r><w:t>; and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>x^4+4x^3+6x^2+4x+1=(x+1)^4</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Therefore the function output should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>7</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 384px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">A polynomial of the form: </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="287.5" height="21" style="width: 287.5px; height: 21px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, is said to be natural factorable if it can be factored into products of first degree binomials: </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="214.5" height="20" style="width: 214.5px; height: 20px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, where, </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="140" height="20" style="width: 140px; height: 20px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> and </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="131.5" height="20" style="width: 131.5px; height: 20px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> are </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="text-decoration: underline; text-decoration-line: underline; ">all</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> natural numbers (i.e. integers that are </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="25" height="18" style="width: 25px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">).</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Given an integer </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">a</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="67.5" height="20" style="width: 67.5px; height: 20px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For example, when </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, the are </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);">7</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> possible natural factorable polynomials, namely:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                                    </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="139" height="20" style="width: 139px; height: 20px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">;</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                                    </span></span><span style="vertical-align:-5px"><img 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</span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="212.5" height="20" style="width: 212.5px; height: 20px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">Therefore the function output should be </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);">7</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">.</span></span></div></div></div>

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Problem 52861. Easy Sequences 37: Natural Factorable Polynomials

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Problem 52861. Easy Sequences 37: Natural Factorable Polynomials

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