{"id":1634,"date":"2019-07-30T13:30:46","date_gmt":"2019-07-30T17:30:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1634"},"modified":"2019-07-30T14:01:28","modified_gmt":"2019-07-30T18:01:28","slug":"answer-key-8-3","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-3\/","title":{"raw":"Answer Key 8.3","rendered":"Answer Key 8.3"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(12a^4b^5\\)<\/li>\r\n \t
  2. \\(25x^3y^5z\\)<\/li>\r\n \t
  3. \\(x(x-3)\\)<\/li>\r\n \t
  4. \\(4(x-2)\\)<\/li>\r\n \t
  5. \\((x+2)(x-4)\\)<\/li>\r\n \t
  6. \\(x(x-7)(x+1)\\)<\/li>\r\n \t
  7. \\((x+5)(x-5)\\)<\/li>\r\n \t
  8. \\((x+3)(x-3)^2\\)<\/li>\r\n \t
  9. \\((x+1)(x+2)(x+3)\\)<\/li>\r\n \t
  10. \\((x-5)(x-2)(x+3)\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&10a^3b^2 \\\\ \\\\\r\n\\dfrac{3a}{5b^2}\\cdot \\dfrac{2a^3}{2a^3} &\\Rightarrow &\\dfrac{6a^4}{10a^3b^2} \\\\ \\\\\r\n\\dfrac{2}{10a^3b}\\cdot \\dfrac{b}{b} &\\Rightarrow & \\dfrac{2b}{10a^3b^2}\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-4)(x+2) \\\\ \\\\\r\n\\dfrac{3x}{(x-4)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{3x^2+6x}{(x-4)(x+2)} \\\\ \\\\\r\n\\dfrac{2}{(x+2)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{2x-8}{(x-4)(x+2)}\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-3)(x+2) \\\\ \\\\\r\n\\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)} \\\\ \\\\\r\n\\dfrac{(x-3)}{(x+2)}\\cdot \\dfrac{(x-3)}{(x-3)}&\\Rightarrow &\\dfrac{x^2-6x+9}{(x-3)(x+2)}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&x(x-6) \\\\ \\\\\r\n\\dfrac{5}{x^2-6x}&\\Rightarrow &\\dfrac{5}{x(x-6)} \\\\ \\\\\r\n\\dfrac{2}{x}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x-12}{x(x-6)} \\\\ \\\\\r\n\\dfrac{-3}{(x-6)}\\cdot \\dfrac{x}{x}&\\Rightarrow & \\dfrac{-3x}{x(x-6)}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-4)^2(x+4) \\\\ \\\\\r\n\\dfrac{x}{x^2-16}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{x^2-4x}{(x-4)^2(x+4)} \\\\ \\\\\r\n\\dfrac{3x}{(x^2-8x+16)}\\cdot \\dfrac{(x+4)}{(x+4)}&\\Rightarrow &\\dfrac{3x^2+12}{(x-4)^2(x+4)}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-5)(x+2) \\\\ \\\\\r\n\\dfrac{5x+1}{x^2-3x-10}&\\Rightarrow &\\dfrac{5x+1}{(x-5)(x+2)} \\\\ \\\\\r\n\\dfrac{4}{(x-5)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{4x+8}{(x-5)(x+2)}\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x+6)^2(x-6) \\\\ \\\\\r\n\\dfrac{x+1}{x^2-36}\\cdot \\dfrac{(x+6)}{(x+6)}&\\Rightarrow &\\dfrac{x^2+7x+6}{(x+6)^2(x-6)} \\\\ \\\\\r\n\\dfrac{(2x+3)}{(x^2+12x+36)}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x^2-9x-18}{(x+6)^2(x-6)}\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-4)(x+3)(x+1) \\\\ \\\\\r\n\\dfrac{(3x+1)}{(x^2-x-12)}\\cdot \\dfrac{(x+1)}{(x+1)}&\\Rightarrow & \\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)} \\\\ \\\\\r\n\\dfrac{2x}{(x^2+4x+3)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-3)(x+2) \\\\ \\\\\r\n\\dfrac{4x}{x^2-x-6}&\\Rightarrow &\\dfrac{4x}{(x-3)(x+2)} \\\\ \\\\\r\n\\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)}\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x-4)(x-2)(x+5) \\\\ \\\\\r\n\\dfrac{3x}{x^2-6x+8}\\cdot \\dfrac{(x+5)}{(x+5)}&\\Rightarrow & \\dfrac{3x^2+15x}{(x-4)(x-2)(x+5)} \\\\ \\\\\r\n\\dfrac{(x-2)}{(x^2+x-20)}\\cdot \\dfrac{(x-2)}{(x-2)}&\\Rightarrow & \\dfrac{x^2-4x+4}{(x-4)(x-2)(x+5)} \\\\ \\\\\r\n\\dfrac{5}{(x^2+3x-10)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{5x-20}{(x-4)(x-2)(x+5)}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"12a^4b^5\"<\/li>\n
    2. \"25x^3y^5z\"<\/li>\n
    3. \"x(x-3)\"<\/li>\n
    4. \"4(x-2)\"<\/li>\n
    5. \"(x+2)(x-4)\"<\/li>\n
    6. \"x(x-7)(x+1)\"<\/li>\n
    7. \"(x+5)(x-5)\"<\/li>\n
    8. \"(x+3)(x-3)^2\"<\/li>\n
    9. \"(x+1)(x+2)(x+3)\"<\/li>\n
    10. \"(x-5)(x-2)(x+3)\"<\/li>\n
    11. \"\begin{array}{rrl}<\/li>\n
    12. \"\begin{array}{rrl}<\/li>\n
    13. \"\begin{array}{rrl}<\/li>\n
    14. \"\begin{array}{rrl}<\/li>\n
    15. \"\begin{array}{rrl}<\/li>\n
    16. \"\begin{array}{rrl}<\/li>\n
    17. \"\begin{array}{rrl}<\/li>\n
    18. \"\begin{array}{rrl}<\/li>\n
    19. \"\begin{array}{rrl}<\/li>\n
    20. \"\begin{array}{rrl}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":71,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1634","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1634\/revisions"}],"predecessor-version":[{"id":1637,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1634\/revisions\/1637"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1634\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1634"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1634"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1634"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}