Let’s simplify and factor the expression:<\/p>\n\n\n\n
Given expression:<\/strong>3Z2+5\u22c56Z5+15Z4+16Z3+4Z2+10Z\u2212353Z^2 + 5 \\cdot 6Z^5 + 15Z^4 + 16Z^3 + 4Z^2 + 10Z – 353Z2+5\u22c56Z5+15Z4+16Z3+4Z2+10Z\u221235<\/p>\n\n\n\n Multiply the constants:5\u22c56Z5=30Z55 \\cdot 6Z^5 = 30Z^55\u22c56Z5=30Z5<\/p>\n\n\n\n Now rewrite the full expression in descending order of powers:30Z5+15Z4+16Z3+4Z2+10Z\u221235+3Z230Z^5 + 15Z^4 + 16Z^3 + 4Z^2 + 10Z – 35 + 3Z^230Z5+15Z4+16Z3+4Z2+10Z\u221235+3Z2<\/p>\n\n\n\n Combine like terms:30Z5+15Z4+16Z3+(4Z2+3Z2)+10Z\u22123530Z^5 + 15Z^4 + 16Z^3 + (4Z^2 + 3Z^2) + 10Z – 3530Z5+15Z4+16Z3+(4Z2+3Z2)+10Z\u22123530Z5+15Z4+16Z3+7Z2+10Z\u22123530Z^5 + 15Z^4 + 16Z^3 + 7Z^2 + 10Z – 3530Z5+15Z4+16Z3+7Z2+10Z\u221235<\/p>\n\n\n\n 30Z5+15Z4+16Z3+7Z2+10Z\u22123530Z^5 + 15Z^4 + 16Z^3 + 7Z^2 + 10Z – 3530Z5+15Z4+16Z3+7Z2+10Z\u221235<\/p>\n\n\n\n To simplify and factor polynomials, the expression should first be organized in descending order of degree<\/strong>, with all like terms combined. This ensures clarity and correctness in further algebraic manipulation. In the given expression, the term Once simplified, the polynomial becomes:30Z5+15Z4+16Z3+7Z2+10Z\u22123530Z^5 + 15Z^4 + 16Z^3 + 7Z^2 + 10Z – 3530Z5+15Z4+16Z3+7Z2+10Z\u221235<\/p>\n\n\n\n This is a 5th-degree polynomial with six terms. Such expressions are called polynomials of higher degree<\/strong> and can sometimes be factored by grouping or using polynomial division. A good first step is to look for a greatest common factor (GCF)<\/strong>. Here, no GCF exists across all terms, so factoring by grouping is attempted.<\/p>\n\n\n\n Group terms strategically:<\/p>\n\n\n\n Factoring each group:<\/p>\n\n\n\n Since the factored parts are not the same, factoring further is not straightforward. This suggests the polynomial may not factor nicely over integers<\/strong> and could require more advanced methods like rational root theorem<\/strong>, synthetic division<\/strong>, or numerical methods.<\/p>\n\n\n\n In conclusion, the expression simplifies to:30Z5+15Z4+16Z3+7Z2+10Z\u221235\\boxed{30Z^5 + 15Z^4 + 16Z^3 + 7Z^2 + 10Z – 35}30Z5+15Z4+16Z3+7Z2+10Z\u221235\u200b<\/p>\n\n\n\n It does not factor easily, and unless specific instructions suggest further factoring, the simplified form is the final result.<\/p>\n\n\n\n 3Z^2 + 5 * 6Z^5 + 15Z^4 + 16Z^3 + 4Z^2 + 10Z – 35 The Correct Answer and Explanation is: Let’s simplify and factor the expression: Given expression:3Z2+5\u22c56Z5+15Z4+16Z3+4Z2+10Z\u2212353Z^2 + 5 \\cdot 6Z^5 + 15Z^4 + 16Z^3 + 4Z^2 + 10Z – 353Z2+5\u22c56Z5+15Z4+16Z3+4Z2+10Z\u221235 Step 1: Simplify the expression Multiply the constants:5\u22c56Z5=30Z55 \\cdot 6Z^5 = 30Z^55\u22c56Z5=30Z5 […]<\/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 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1: Simplify the expression<\/h3>\n\n\n\n
\n\n\n\nFinal simplified polynomial:<\/h3>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n
5 * 6Z^5<\/code> is a product that must be evaluated before combining with the rest of the polynomial. Multiplying gives 30Z^5<\/code>.<\/p>\n\n\n\n\n
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