{"id":271,"date":"2023-04-30T10:00:58","date_gmt":"2023-04-30T04:30:58","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=271"},"modified":"2023-05-01T09:38:23","modified_gmt":"2023-05-01T04:08:23","slug":"factors-and-coefficients-of-a-polynomial","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/factors-and-coefficients-of-a-polynomial\/","title":{"rendered":"Factors And Coefficients Of A Polynomial"},"content":{"rendered":"<h2>Factors And Coefficients Of A Polynomial<\/h2>\n<p><strong>Factor:\u00a0 <\/strong><br \/>\nWhen numbers (constants) and variables are multiplied to form a term, then each quantity multiplied is called a <strong>factor<\/strong> of the term. A constant factor is called a numerical factor while a variable factor is called a literal factor.<\/p>\n<p><strong>For Example:<\/strong><br \/>\n(i)\u00a0\u00a0 7, x and 7x are factors of 7x, in which<br \/>\n7 is constant (numerical) factor and x is variable (literal) factor.<br \/>\n(ii)\u00a0 In 5x<sup>2<\/sup>y, the numerical factor is \u20135 and literal factors are : x, y, xy, x<sup>2<\/sup>\u00a0and x<sup>2<\/sup>y.<\/p>\n<p><strong>Coefficient: <\/strong><br \/>\nAny factor of a term is called the <strong>coefficient<\/strong> of the product of the remaining factors.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128283\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-1.jpg\" alt=\"Factors And Coefficients Of A Polynomial 1\" width=\"632\" height=\"346\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-1.jpg 632w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-1-300x164.jpg 300w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-1-630x346.jpg 630w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><br \/>\nThere are two types of coefficients:<br \/>\n1. Numerical coefficient or simply coefficient<br \/>\n2. Literal coefficient<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12851\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/factors-and-coefficients-of-a-polynomial-1-3.jpg\" alt=\"\" width=\"544\" height=\"389\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/factors-and-coefficients-of-a-polynomial-1-3.jpg 544w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/factors-and-coefficients-of-a-polynomial-1-3-300x215.jpg 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/V3HejxzKIR8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>For Example:<\/strong><br \/>\n(i)\u00a0\u00a0 In 7x ; 7 is coefficient of x<br \/>\n(ii) In 7xy, the numerical coefficient of the term 7xy is 7 and the literal coefficient is xy.<br \/>\nIn a more general way,<br \/>\nCoefficient of xy = 7<br \/>\nCoefficient of 7x = y<br \/>\nCoefficient of 7y = x<br \/>\n(iii) In (- mn<sup>2<\/sup>), the numerical coefficient of the term is (- 1) and the literal coefficient is mn<sup>2<\/sup>.<br \/>\nIn a more general way,<br \/>\nCoefficient of mn<sup>2<\/sup>\u00a0= &#8211; 1<br \/>\nCoefficient of (-n<sup>2<\/sup>) = m<br \/>\nCoefficient of m = (- n<sup>2<\/sup>)<br \/>\n(iv)\u00a0 In \u20135x<sup>2<\/sup>y; 5 is coefficient of \u00ad\u2013x<sup>2<\/sup>y; \u20135 is coefficient of x<sup>2<\/sup>y.<\/p>\n<p><strong>Like and unlike terms:<\/strong> Two or more terms having the same algebraic factors are called like terms, and two or more terms having different algebraic factors are called unlike terms.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128284\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-2.jpg\" alt=\"Factors And Coefficients Of A Polynomial 2\" width=\"632\" height=\"331\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-2.jpg 632w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-2-300x157.jpg 300w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-2-630x331.jpg 630w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128286\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-3.jpg\" alt=\"Factors And Coefficients Of A Polynomial 3\" width=\"634\" height=\"327\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-3.jpg 634w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Factors-And-Coefficients-Of-A-Polynomial-3-300x155.jpg 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><\/p>\n<p><strong>Example:<\/strong> In the expression 5x<sup>2<\/sup> + 7xy &#8211; 7y &#8211; 5xy, look at the terms 7xy and (- 5xy). The factors of 7xy are 7, x, and y and the factors of (- 5xy) are (- 5), x, and y. The algebraic factors (which contain variables) of both terms are x and y. Hence, they are like terms. Other terms 5x<sup>2<\/sup>\u00a0and (- 7y) have different algebraic factors [5 \u00d7\u00a0x \u00d7\u00a0x and (- 7y)]. Hence, they are unlike terms.<\/p>\n<h2>Factors And Coefficients Of A Polynomial With Examples<\/h2>\n<p><strong>Example 1: \u00a0 \u00a0<\/strong>Write the coefficient of:<br \/>\n(i) \u00a0 x<sup>2<\/sup>\u00a0in 3x<sup>3<\/sup> \u2013 5x<sup>2<\/sup> + 7<br \/>\n(ii)\u00a0 xy in 8xyz<br \/>\n(iii) \u2013y in 2y<sup>2<\/sup> \u2013 6y + 2<br \/>\n(iv) x<sup>0<\/sup>\u00a0in 3x + 7<br \/>\n<strong>Solution:<\/strong><br \/>\n(i) \u20135<br \/>\n(ii) 8z<br \/>\n(iii) 6<br \/>\n(iv) Since x<sup>0<\/sup>\u00a0= 1,<br \/>\nTherefore\u00a03x + 7 = 3x + 7x<sup>0<\/sup><br \/>\ncoefficient of x<sup>0<\/sup>\u00a0is 7.<\/p>\n<p><strong>Example 2:<\/strong> Identify like terms in the following:<br \/>\n2xy, -xy<sup>2<\/sup>, x<sup>2<\/sup>y, 5y, 8yx, 12yx<sup>2<\/sup>, -11xy<br \/>\n<strong>Solution:<\/strong> \u00a02xy, 8yx, -11xy are like terms having the same algebraic factors x and y.<br \/>\nx<sup>2<\/sup>y and 12yx<sup>2<\/sup> are also like terms having the same algebraic factors x, x and y.<\/p>\n<p><strong>Example 3:<\/strong> State whether the given pairs of terms are like or unlike terms:<br \/>\n(a) 19x, 19y (b) 4m<sup>2<\/sup>p, 7pm<sup>2<\/sup><br \/>\n<strong>Solution:<\/strong><br \/>\n(a) 19x and 19y are unlike terms having different algebraic factors, i.e., x and y.<br \/>\n(b) 4m<sup>2<\/sup>p, 7pm<sup>2<\/sup> are like terms having the same algebraic factors, i.e., m, m, p.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Factors And Coefficients Of A Polynomial Factor:\u00a0 When numbers (constants) and variables are multiplied to form a term, then each quantity multiplied is called a factor of the term. A constant factor is called a numerical factor while a variable factor is called a literal factor. For Example: (i)\u00a0\u00a0 7, x and 7x are factors [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[32,31,33,2391,24],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Factors And Coefficients Of A Polynomial - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/factors-and-coefficients-of-a-polynomial\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Factors And Coefficients Of A Polynomial\" \/>\n<meta property=\"og:description\" content=\"Factors And Coefficients Of A Polynomial Factor:\u00a0 When numbers (constants) and variables are multiplied to form a term, then each quantity multiplied is called a factor of the term. 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