[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-461865-105":59,"doc-detail-461865-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","algebra-practice-problems-for-precalculus-and-calculus","Algebra Practice Problems for Precalculus and Calculus","","Practice set of algebra problems focused on solving equations for an unknown x, multiplying polynomials and simplifying, finding domains of radical and rational functions, and factoring quadratic expressions. Includes a three-method approach for solving quadratics using factoring, the quadratic formula, and completing the square, plus mixed exercises involving equations, inequalities, and square-root notation. Also covers adding, subtracting, and simplifying rational expressions, followed by worked solutions and domain-checking guidance.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/algebra-practice-problems-for-precalculus-and-calculus/461865/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/algebra-practice-problems-for-precalculus-and-calculus/461865.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What types of problems are included in this algebra practice set?","Question",{"text":113,"@type":114},"It includes solving equations for x, multiplying and simplifying polynomials, determining domains of functions, factoring quadratics, and adding/subtracting/simplifying rational expressions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are quadratic equations intended to be solved?",{"text":118,"@type":114},"Quadratic equations are solved in three ways: factoring, using the quadratic formula, and completing the square.",{"name":120,"@type":111,"acceptedAnswer":121},"Why does the document emphasize checking solutions and domain restrictions?",{"text":122,"@type":114},"Because dividing by expressions involving x can introduce invalid values (like division by zero), and functions such as square roots require nonnegative quantities, so checking ensures the result satisfies the original equation and valid domain.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},461865,1790795092,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","Algebra Practice Problems for Precalculus and Calculus  \nSolve the following equations for the unknown x:  \n1. 5 D 7x 􀀀 16  \n2. 2x 􀀀 3 D 5 􀀀 x  \n3. 12 .x 􀀀 3/ C x D 17 C 3.4 􀀀 x/  \n4. 5x D x~~ ~~3  \nMultiply the indicated polynomials and simplify.  \n5. .4x 􀀀 1/.􀀀3x C 2/  \n6. .x 􀀀 1/.x2 C x C 1/  \n7. .x C 1/.x2 􀀀 x C 1/  \n8. .x 􀀀 2/.x C 2/  \n9. .x 􀀀 2/.x 􀀀 2/  \n10. .x3 C 2x 􀀀 1/.x3 􀀀 5x2 C 4/  \nFind the domain of each of the following functions in 11-15.  \n11. f .x/ D p1 C x  \n12. f .x/ D 11Cx  \n13. f .x/ D 1px  \n14. f .x/ D p11Cx  \n15. f .x/ D 11Cx2  \n16. Given that f .x/ D x 2 􀀀 3x C 4, find and simplify f .3/; f .a/; f .􀀀t/, and f .x2 C 1/ .  \nFactor the following quadratics  \n17. x 2 􀀀 x 􀀀 20  \n18. x 2 􀀀 10x C 21  \n19. x 2 C 10x C 16  \n20. x 2 C 8x 􀀀 105  \n21. 4x2 C 11x 􀀀 3  \n22. 􀀀2x2 C 7x C 15  \n23. x 2 􀀀 2  \nSolve the following quadratic equations in three ways: 1) factor, 2) quadratic formula, 3) complete the square  \n24. x 2 C 6x 􀀀 16 D 0  \n25. 􀀀x2 􀀀 3x 􀀀 2 D 0  \n26. 2x2 C 2x 􀀀 4 D 0  \nSolve the following smorgasbord of equations and inequalities  \n27. px D p2x 􀀀 1  \n28. px 2 􀀀 3 D p2x  \n29. jx 􀀀 5j D 4  \n30. 2x C 4 􀀕 3  \n31. 􀀀2x C 4 􀀕 3  \n32. xx43 D 2  \n33. x 2 􀀀 x 􀀀 2 > 0  \nAdd/Subtract the following rational expressions:  \n34. x~~ ~~xC2 C x~~ ~~4  \n35. .x~~ ~~􀀀x21/Cx1􀀀2/ 􀀀 x3  \nSimplify the following rational expressions (if possible):  \n36. x2 Cx􀀀2 x 2 􀀀1  \n37. x2 C5xC6 x2 􀀀3xC2  \n38.  \nx~~ ~~xC2 C 3  \nxC1  \nx􀀀1  \nSolutions  \n1. Given that 5 D 7x 􀀀 16, add 16 to both sides to get 7x D 21. Now divide both sides by 7 to get x D 3. Checking, we see that 7.3/ 􀀀 16 D 21 􀀀 16 D 5.  \n2. Given that 2x 􀀀 3 D 5 􀀀 x , add x to both sides and then add 3 to both sides to get 3x D 8. Now divide both sides by 3 to get x D 8=3 D 2: . Checking, we see that 2.8=3/ 􀀀 3 D 136 􀀀 3 D 136 􀀀 93 D 73 and 5 􀀀 .8=3/ D 135 􀀀 83 D 73 .  \n3. Given that 12 .x 􀀀 3/ C x D 17 C 3.4 􀀀 x/, we first simplify the left and right hand sides using the distributive property to get 12 x 􀀀 32 C x D 17 C 12 􀀀 3x . Combining like terms on both sides gives 32 x 􀀀 32 D 29 􀀀 3x . Now we add 3x and 32 to both sides, obtaining 92 x D 621 . Dividing both sides by 92 (or multiplying both sides by 29 ) gives x D 621 􀀁 29 D 691 . Checking we see that LH S D 12 . 691 􀀀 297 / C 691 D 1 342 ~~ ~~9 C 691 D 197 C 691 D 798 and RH S D 17 C 3. 396 􀀀 691 / D 17 C 3 􀀁 􀀐 􀀀259 􀀑 D 17 􀀀 795 D  \n153 75 78  \n~~ ~~ 􀀀 ~~ ~~ D ~~ ~~  \n9 9 9 .  \n4. Given that 5x D x~~ ~~3 , we “cross-multiply” to obtain 5.x 􀀀 3/ D 2x . Distributing the 5 gives 5x 􀀀 15 D 2x . Subtracting 2x and adding 15 to both sides gives 3x D 15. Dividing both sides by 3 gives x D 5. Checking, we see that 55 D 1 and 53 D 22 D 1. NOTE: Checking is very important in this kind of problem. When there are x ’s in the denominator of fractions in equations, it is possible that your final “solution” doesn’t satisfy the original equation (because you would divide by zero)–so it is really not a solution to the original problem.  \nIn the “multiply and simplify” problems, we must multiply each term in the left-hand factor with each term in the right-hand factor, and then simplify by combining like terms. In the case of binomial 􀀂 binomial , we can use the so-called FOIL method.  \n5. .4x 􀀀 1/.􀀀3x C 2/ D 􀀀12x2 C 8x C 3x 􀀀 2 D 􀀀12x2 C 11x 􀀀 2.  \n6. .x 􀀀 1/.x2 C x C 1/ D x 3 C x 2 C x 􀀀 x 2 􀀀 x 􀀀 1 D x 3 􀀀 1.  \n7. .x C 1/.x2 􀀀 x C 1/ D x 3 􀀀 x 2 C x C x 2 􀀀 x C 1 D x 3 C 1.  \n8. .x 􀀀 2/.x C 2/ D x 2 C 2x 􀀀 2x 􀀀 4 D x 2 􀀀 4.  \n9. .x 􀀀 2/.x 􀀀 2/ D x 2 􀀀 2x 􀀀 2x C 4 D x 2 􀀀 4x C 4.  \n10. .x3 C 2x 􀀀 1/.x3 􀀀 5x2 C 4/ D x 6 􀀀 5x5 C 4x3 C 2x4 􀀀 10x3 C 8x 􀀀 x 3 C 5x2 􀀀 4 D x 6 􀀀 5x5 C 2x4 􀀀 7x3 C 5x2 C 8x 􀀀 4  \n11. For a number x to be in the domain of the function f .x/ D p1 C x  , we require 1 C x 􀀕 0 (so we don’t take the square root of a negative number) . Subtracting 1 from both sides of this inequality yields x 􀀕 􀀀1. Thus, in interval notation, the domain is theset T􀀀1 ; 1/ .  \n12. For a number x to be in the domain of the function f .x/ D","cbCaiifJv2YXqrQB","https://ap.wps.com/l/cbCaiifJv2YXqrQB","pdf",55505,"English","# Solve Equations for x\n## Multiply and Simplify Polynomials\n## Find Function Domains\n## Evaluate f(x) for Given Inputs\n## Factor Quadratics\n## Solve Quadratic Equations (Three Methods)\n## Solve Equations and Inequalities\n## Add/Subtract Rational Expressions\n## Simplify Rational Expressions\n# Solutions","[{\"question\":\"What types of problems are included in this algebra practice set?\",\"answer\":\"It includes solving equations for x, multiplying and simplifying polynomials, determining domains of functions, factoring quadratics, and adding/subtracting/simplifying rational expressions.\"},{\"question\":\"How are quadratic equations intended to be solved?\",\"answer\":\"Quadratic equations are solved in three ways: factoring, using the quadratic formula, and completing the square.\"},{\"question\":\"Why does the document emphasize checking solutions and domain restrictions?\",\"answer\":\"Because dividing by expressions involving x can introduce invalid values (like division by zero), and functions such as square roots require nonnegative quantities, so checking ensures the result satisfies the original equation and valid domain.\"}]","Algebra Practice Problems for Precalculus and Calculus | PDF",1790762626,15]