{"id":38861,"date":"2025-06-26T14:02:53","date_gmt":"2025-06-26T14:02:53","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=38861"},"modified":"2025-06-26T14:02:54","modified_gmt":"2025-06-26T14:02:54","slug":"consider-the-following-polynomial","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/consider-the-following-polynomial\/","title":{"rendered":"Consider the following polynomial"},"content":{"rendered":"\n
Consider the following polynomial: -9 + x4 – 5x + 2×3 + 5x This polynomial can be classified as fifth degree. fourth degree. monomial. binomial. trinomial.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To classify the polynomial, we need to follow these steps:<\/p>\n\n\n\n
Step 1: Combine like terms and arrange in standard form<\/strong><\/h4>\n\n\n\n
The given polynomial is: \u22129+x4\u22125x+2×3+5x-9 + x^4 – 5x + 2x^3 + 5x\u22129+x4\u22125x+2×3+5x<\/p>\n\n\n\n
First, combine like terms. Notice that -5x and +5x<\/strong> cancel each other out: \u22129+x4+2×3-9 + x^4 + 2x^3\u22129+x4+2×3<\/p>\n\n\n\n
Now arrange in descending order of exponents<\/strong>: x4+2×3\u22129x^4 + 2x^3 – 9×4+2×3\u22129<\/p>\n\n\n\n
Step 2: Determine the degree<\/strong><\/h4>\n\n\n\n
The degree<\/strong> of a polynomial is the highest power of the variable. In this simplified expression: x4+2×3\u22129x^4 + 2x^3 – 9×4+2×3\u22129<\/p>\n\n\n\n
The highest exponent is 4<\/strong>, from the term x\u2074<\/strong>, so the degree is 4<\/strong>. Therefore, the polynomial is classified as a fourth-degree<\/strong> polynomial.<\/p>\n\n\n\n
Step 3: Count the number of terms<\/strong><\/h4>\n\n\n\n
A polynomial\u2019s type can also be described by the number of non-zero terms<\/strong>:<\/p>\n\n\n\n
The simplified version has three terms:<\/p>\n\n\n\n
\n
x4x^4×4<\/li>\n\n\n\n
2x32x^32×3<\/li>\n\n\n\n
\u22129-9\u22129<\/li>\n<\/ol>\n\n\n\n
So, the polynomial is a trinomial<\/strong>.<\/p>\n\n\n\n
Conclusion<\/strong><\/h4>\n\n\n\n
Putting the classification together:<\/p>\n\n\n\n
\n
The degree<\/strong> is 4<\/li>\n\n\n\n
There are 3 terms<\/strong><\/li>\n<\/ul>\n\n\n\n
Thus, the polynomial is a fourth-degree trinomial<\/strong>.<\/p>\n\n\n\n
This classification helps in understanding the behavior of the polynomial, especially when graphing or solving. Higher-degree polynomials can have more turning points, and identifying the number of terms simplifies factoring and operations.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Consider the following polynomial: -9 + x4 – 5x + 2×3 + 5x This polynomial can be classified as fifth degree. fourth degree. monomial. binomial. trinomial. The Correct Answer and Explanation is: Correct Answer: Fourth degree trinomial Explanation: To classify the polynomial, we need to follow these steps: Step 1: Combine like terms and arrange […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38861","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38861"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38861\/revisions"}],"predecessor-version":[{"id":38863,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38861\/revisions\/38863"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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