{"id":217179,"date":"2025-05-21T06:49:02","date_gmt":"2025-05-21T06:49:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217179"},"modified":"2025-05-21T06:49:04","modified_gmt":"2025-05-21T06:49:04","slug":"which-of-the-following-are-polynomial-functions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/which-of-the-following-are-polynomial-functions\/","title":{"rendered":"Which of the following are polynomial functions"},"content":{"rendered":"\n

Please tell me the polynomials and why are they polynomials. Thank you for your time.<\/p>\n\n\n\n

Which of the following are polynomial functions?<\/p>\n\n\n\n

f(x) = 0
f(x) = -9
f(x) = 3 + 1
f(x) = 1\/2 + 8
f(x) = 32 + 2
f(x) = 45\/84<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s examine each of the following functions to determine which are polynomial functions<\/strong> and explain why.<\/p>\n\n\n\n

\n\n\n\n

What is a Polynomial Function?<\/strong><\/h3>\n\n\n\n

A polynomial function<\/strong> is a mathematical expression involving a sum of powers of the variable x<\/strong> with real number coefficients. A general form is: f(x)=anxn+an\u22121xn\u22121+\u2026+a1x+a0f(x) = a_nx^n + a_{n-1}x^{n-1} + \\ldots + a_1x + a_0<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • an,an\u22121,\u2026,a0a_n, a_{n-1}, \\ldots, a_0 are real numbers (called coefficients),<\/li>\n\n\n\n
  • nn is a non-negative integer (no negative or fractional exponents),<\/li>\n\n\n\n
  • The variable xx is raised to whole-number powers only.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Let\u2019s evaluate each function:<\/strong><\/h3>\n\n\n\n
      \n
    1. f(x) = 0<\/strong>
      \u2705 Polynomial<\/strong>
      This is a zero polynomial<\/strong>, which is valid because it can be written as 0x00x^0. It has no variable terms, but 0 is considered a constant polynomial.<\/li>\n\n\n\n
    2. f(x) = -9<\/strong>
      \u2705 Polynomial<\/strong>
      This is a constant polynomial<\/strong>, which is valid and has degree 0 (no variable, just a constant). Constants are polynomials.<\/li>\n\n\n\n
    3. f(x) = 3 + 1<\/strong>
      \u2705 Polynomial<\/strong>
      This simplifies to f(x)=4f(x) = 4, a constant. As above, constants are polynomials of degree 0.<\/li>\n\n\n\n
    4. f(x) = 1\/2 + 8<\/strong>
      \u2705 Polynomial<\/strong>
      This simplifies to f(x)=8.5f(x) = 8.5 or 172\\frac{17}{2}. It is a constant polynomial \u2014 again, valid.<\/li>\n\n\n\n
    5. f(x) = 32 + 2<\/strong>
      \u2705 Polynomial<\/strong>
      This simplifies to f(x)=34f(x) = 34. Constant again \u2014 a polynomial.<\/li>\n\n\n\n
    6. f(x) = 45\/84<\/strong>
      \u2705 Polynomial<\/strong>
      This simplifies to f(x)=1528f(x) = \\frac{15}{28}, a constant. Any real number constant is a polynomial of degree 0.<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      \u2705 Final Answer: All of them are polynomial functions.<\/strong><\/h3>\n\n\n\n
      \n\n\n\n

      Why Are They Polynomials?<\/strong><\/h3>\n\n\n\n

      Even though these functions don\u2019t involve a variable (like xx), they are still polynomials. Polynomials include:<\/p>\n\n\n\n

        \n
      • Zero<\/strong> (like f(x)=0f(x) = 0),<\/li>\n\n\n\n
      • Constants<\/strong> (like f(x)=\u22129f(x) = -9, f(x)=172f(x) = \\frac{17}{2}, or any real number),<\/li>\n\n\n\n
      • Or expressions like f(x)=axn+bxn\u22121+\u2026f(x) = ax^n + bx^{n-1} + \\ldots (none of which appear here, but would still qualify).<\/li>\n<\/ul>\n\n\n\n

        There are no variables raised to a negative or fractional exponent<\/strong>, no variables inside square roots, and all the coefficients are real numbers \u2014 these are the key rules that define a polynomial. Since all examples here are constants and constants are polynomials (specifically, of degree 0), they are all valid polynomial functions<\/strong>.<\/p>\n\n\n\n

        Let me know if you want examples of non-polynomials for contrast!<\/p>\n","protected":false},"excerpt":{"rendered":"

        Please tell me the polynomials and why are they polynomials. Thank you for your time. Which of the following are polynomial functions? f(x) = 0f(x) = -9f(x) = 3 + 1f(x) = 1\/2 + 8f(x) = 32 + 2f(x) = 45\/84 The Correct Answer and Explanation is: Let’s examine each of the following functions to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-217179","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=217179"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217179\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}