{"id":13337,"date":"2020-12-10T07:50:17","date_gmt":"2020-12-10T02:20:17","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13337"},"modified":"2020-12-10T11:03:06","modified_gmt":"2020-12-10T05:33:06","slug":"polynomials","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/polynomials\/","title":{"rendered":"Polynomials"},"content":{"rendered":"<h2>Polynomials<\/h2>\n<p>Algebraic expression containing many terms of the form ax<sup>n<\/sup>, n being a non-negative integer is called a polynomial. i.e., f(x) = a<sub>0<\/sub> + a<sub>1<\/sub>x + a<sub>2<\/sub>x<sup>2<\/sup> + a<sub>3<\/sub>x<sup>3<\/sup> + \u2026\u2026.. + a<sub>n-1<\/sub>x<sup>n-1<\/sup> + a<sub>n<\/sub>x<sub>n<\/sub>, where x is a variable, a<sub>0<\/sub>, a<sub>1<\/sub>, a<sub>2<\/sub>, \u2026\u2026 a<sub>n<\/sub>\u00a0are constants and a<sub>n<\/sub> \u2260 0.<br \/>\n<strong>Example:<\/strong> 4x<sup>4<\/sup> + 3x<sup>3<\/sup> \u2013 7x<sup>2<\/sup> + 5x + 3, 3x<sup>3<\/sup> + x<sup>2<\/sup> \u2013 3x + 5.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128778 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polynomials-1.jpg\" alt=\"Polynomials 1\" width=\"702\" height=\"461\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polynomials-1.jpg 702w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Polynomials-1-300x197.jpg 300w\" sizes=\"(max-width: 702px) 100vw, 702px\" \/><br \/>\n<strong>(1) Real polynomial:<\/strong><br \/>\nf(x) = a<sub>0<\/sub> + a<sub>1<\/sub>x + a<sub>2<\/sub>x<sup>2<\/sup> + a<sub>3<\/sub>x<sup>3<\/sup> + \u2026\u2026.. + a<sub>n<\/sub>x<sub>n\u00a0<\/sub>is called real polynomial of real variable x with real coefficients.<br \/>\n<strong>Example:<\/strong> 3x<sup>3<\/sup> \u2013 4x<sup>2<\/sup> + 5x \u2013 4, x<sup>2<\/sup> \u2013 2x + 1 etc. are real polynomials.<\/p>\n<p><strong>(2) Complex polynomial:<\/strong><br \/>\nf(x) = a<sub>0<\/sub> + a<sub>1<\/sub>x + a<sub>2<\/sub>x<sup>2<\/sup> + a<sub>3<\/sub>x<sup>3<\/sup> + \u2026\u2026.. + a<sub>n<\/sub>x<sub>n<\/sub>\u00a0is called complex polynomial of complex variable x with complex coefficients.<br \/>\n<strong>Example:<\/strong> 3x<sup>2<\/sup> \u2013 (2+4i)x + (5i-4), x<sup>3<\/sup> \u2013 5ix<sup>2<\/sup> + (1+2i)x + 4 etc. are complex polynomials.<\/p>\n<p><strong>(3) Degree of polynomial:<\/strong><br \/>\nHighest power of variable x in a polynomial is called degree of polynomial.<br \/>\n<strong>Example:<\/strong> f(x) = a<sub>0<\/sub> + a<sub>1<\/sub>x + a<sub>2<\/sub>x<sup>2<\/sup> + a<sub>3<\/sub>x<sup>3<\/sup> + \u2026\u2026.. + a<sub>n<\/sub>x<sub>n<\/sub>\u00a0is a n degree polynomial.<br \/>\nf(x) = 4x<sup>3<\/sup> + 3x<sup>2<\/sup> \u2013 7x + 5 is a 3 degree polynomial.<br \/>\nA polynomial of second degree is generally called a quadratic polynomial. Polynomials of degree 3 and 4 are known as cubic and biquadratic polynomials respectively.<\/p>\n<p><strong>(4) Polynomial equation:<\/strong><br \/>\nIf f(x) is a polynomial, real or complex, then f(x) = 0 is called a polynomial equation.<\/p>\n<p><b>Read More:<\/b><\/p>\n<ul>\n<li><a href=\"https:\/\/www.aplustopper.com\/polynomials\/\">What is a Polynomial?<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/types-of-polynomials\/\">Types of Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/monomials-binomials-polynomials\/\">Monomials, Binomials, and Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/adding-polynomials\/\">Adding Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/subtracting-polynomials\/\">Subtracting Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/dividing-polynomials\/\">Dividing Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/division-algorithm-for-polynomials\/\">Polynomials &#8211; Long Division<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/degree-of-a-polynomial\/\">Degree (of an Expression)<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/special-pattern-binomials\/\">Special Binomial Products<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/multiplying-binomials\/\">Multiplying Binomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/algebraic-identities-of-polynomials\/\">Difference of Two Cubes<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/remainder-theorem\/\">Polynomial Remainder Theorem<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/types-of-factorization\/\">Factoring in Algebra<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/factorization-of-polynomials-using-factor-theorem\/\">Factorization of Polynomials Using Factor Theorem<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/factor-theorem\/\">How do you use the factor theorem?<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/factorization-by-splitting-middle-term\/\">How to factorise a polynomial by splitting the middle term?<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/review-factoring-polynomials\/\">Review Factoring Polynomials<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/zeros-of-a-polynomial-function\/\">Zeros of a Polynomial Function<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/factors-and-coefficients-of-a-polynomial\/\">Factors and Coefficients of a Polynomial<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/relationship-between-zeros-and-coefficients-of-a-polynomial\/\">Roots of Polynomials: Sums and Products<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/solving-polynomials-equations-higher-degree\/\">Solving Polynomial Equations of Higher Degree<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/examining-graphs-polynomial-equations-higher-degree\/\">Examining Graphs of Polynomial Equations of Higher Degree<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Polynomials Algebraic expression containing many terms of the form axn, n being a non-negative integer is called a polynomial. i.e., f(x) = a0 + a1x + a2x2 + a3x3 + \u2026\u2026.. + an-1xn-1 + anxn, where x is a variable, a0, a1, a2, \u2026\u2026 an\u00a0are constants and an \u2260 0. Example: 4&#215;4 + 3&#215;3 \u2013 [&hellip;]<\/p>\n","protected":false},"author":5,"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":[4854,4855,4856,24,4853],"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>Polynomials - 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\/polynomials\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polynomials\" \/>\n<meta property=\"og:description\" content=\"Polynomials Algebraic expression containing many terms of the form axn, n being a non-negative integer is called a polynomial. i.e., f(x) = a0 + a1x + a2x2 + a3x3 + \u2026\u2026.. + an-1xn-1 + anxn, where x is a variable, a0, a1, a2, \u2026\u2026 an\u00a0are constants and an \u2260 0. 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