Write a polynomial in factored form with zeros 2,-2, and 1 . Each zero has multiplicity 1.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To construct a polynomial in factored form with given zeros 2, -2, and 1, each with multiplicity 1, follow these steps:<\/p>\n\n\n\n Thus, the polynomial is: P(x)=x3\u2212x2\u22124x+4P(x) = x^3 – x^2 – 4x + 4<\/p>\n\n\n\n Explanation<\/strong>: Write a polynomial in factored form with zeros 2,-2, and 1 . Each zero has multiplicity 1. The correct answer and explanation is: To construct a polynomial in factored form with given zeros 2, -2, and 1, each with multiplicity 1, follow these steps: Thus, the polynomial is: P(x)=x3\u2212x2\u22124x+4P(x) = x^3 – x^2 – 4x […]<\/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-46356","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46356","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=46356"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46356\/revisions"}],"predecessor-version":[{"id":46357,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46356\/revisions\/46357"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
A zero of a polynomial is a value of xx where the polynomial equals zero. The multiplicity of a zero indicates how many times it appears as a factor in the polynomial. For example, a zero of 2 with multiplicity 1 means (x\u22122)(x – 2) appears once as a factor.<\/li>\n\n\n\n
If the zeros are 2, -2, and 1, the corresponding factors of the polynomial are:\n\n
To create the polynomial, multiply all the factors: P(x)=(x\u22122)(x+2)(x\u22121)P(x) = (x – 2)(x + 2)(x – 1)<\/li>\n\n\n\n
First, expand the first two factors, (x\u22122)(x+2)(x – 2)(x + 2), which is a difference of squares: (x\u22122)(x+2)=x2\u22124(x – 2)(x + 2) = x^2 – 4 Now, multiply this result by the third factor, (x\u22121)(x – 1): (x2\u22124)(x\u22121)(x^2 – 4)(x – 1) Use distributive property (FOIL) to expand: =x2(x\u22121)\u22124(x\u22121)= x^2(x – 1) – 4(x – 1) =x3\u2212x2\u22124x+4= x^3 – x^2 – 4x + 4<\/li>\n<\/ol>\n\n\n\n
The polynomial P(x)=(x\u22122)(x+2)(x\u22121)P(x) = (x – 2)(x + 2)(x – 1) is constructed by considering the given zeros and their multiplicities. The factored form (x\u22122)(x+2)(x\u22121)(x – 2)(x + 2)(x – 1) directly corresponds to the zeros 2, -2, and 1. After expanding, we arrive at a cubic polynomial with integer coefficients. The degree of the polynomial is 3, which matches the number of distinct zeros. Each factor corresponds to a unique zero with multiplicity 1, and the expanded form shows the standard polynomial format.<\/p>\n","protected":false},"excerpt":{"rendered":"