{"id":2002,"date":"2021-12-02T19:40:24","date_gmt":"2021-12-03T00:40:24","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-8\/"},"modified":"2022-11-02T10:39:02","modified_gmt":"2022-11-02T14:39:02","slug":"answer-key-10-8","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-8\/","title":{"raw":"Answer Key 10.8","rendered":"Answer Key 10.8"},"content":{"raw":"
    \n \t
  1. [latex]x=5, x=2[\/latex]\n[latex]x-5=0, x-2=0[\/latex][latex]0=(x-5)(x-2)[\/latex]\n[latex]0=x^2-7x+10[\/latex]<\/li>\n \t
  2. [latex]x=3, x=6[\/latex]\n[latex]x-3=0, x-6=0[\/latex][latex](x-3)(x-6)=0[\/latex]\n[latex]0=x^2-9x+18[\/latex]<\/li>\n \t
  3. [latex]x=20, x=2[\/latex]\n[latex]x-20=0, x-2=0[\/latex][latex]0=(x-20)(x-2)[\/latex]\n[latex]0=x^2-22x+40[\/latex]<\/li>\n \t
  4. [latex]x=13, x=1[\/latex]\n[latex]x-13=0, x-1=0[\/latex][latex]0=(x-13)(x-1)[\/latex]\n[latex]0=x^2-14x+13[\/latex]<\/li>\n \t
  5. [latex]x=4, x=4[\/latex]\n[latex]x-4=0, x-4=0[\/latex][latex]0=(x-4)(x-4)[\/latex]\n[latex]0=x^2-8x+16[\/latex]<\/li>\n \t
  6. [latex]x=0, x=9[\/latex]\n[latex]x-9=0, x[\/latex][latex]x(x-9)=0[\/latex]\n[latex]0=x^2-9x[\/latex]<\/li>\n \t
  7. [latex]x=\\dfrac{3}{4}, x=\\dfrac{1}{4}[\/latex]\n[latex]x-\\dfrac{3}{4}=0, x-\\dfrac{1}{4}=0 [\/latex][latex]0=\\left(x-\\dfrac{3}{4}\\right)\\left(x-\\dfrac{1}{4}\\right)[\/latex]\n[latex]0=x^2-x+\\dfrac{3}{16}[\/latex]<\/li>\n \t
  8. [latex]x=\\dfrac{5}{8}, x=\\dfrac{5}{7}[\/latex]\n[latex]x-\\dfrac{5}{8}=0, x-\\dfrac{5}{7}=0[\/latex][latex]0=\\left(x-\\dfrac{5}{8}\\right)\\left(x-\\dfrac{5}{7}\\right)[\/latex]\n[latex]0=x^2-\\dfrac{75}{56}x+\\dfrac{25}{56}[\/latex]<\/li>\n \t
  9. [latex]x=\\dfrac{1}{2}, x=\\dfrac{1}{3}[\/latex]\n[latex]x-\\dfrac{1}{2}=0, x-\\dfrac{1}{3}=0[\/latex][latex]0=\\left(x-\\dfrac{1}{2}\\right)\\left(x-\\dfrac{1}{3}\\right)[\/latex]\n[latex]0=x^2-\\dfrac{5}{6}x+\\dfrac{1}{6}[\/latex]<\/li>\n \t
  10. [latex]x=\\dfrac{1}{2}, x=\\dfrac{2}{3}[\/latex]\n[latex]x-\\dfrac{1}{2}=0, x-\\dfrac{2}{3}=0[\/latex][latex]0=\\left(x-\\dfrac{1}{2}\\right)\\left(x-\\dfrac{2}{3}\\right)[\/latex]\n[latex]0=x^2-\\dfrac{7}{6}x+\\dfrac{1}{3}[\/latex]<\/li>\n \t
  11. [latex]x=5, x=-5[\/latex]\n[latex]x-5=0, x+5=0[\/latex][latex]0=(x-5)(x+5)[\/latex]\n[latex]0=x^2-25[\/latex]<\/li>\n \t
  12. [latex]x=1, x=-1[\/latex]\n[latex]x-1=0, x+1=0[\/latex][latex]0=(x-1)(x+1)[\/latex]\n[latex]0=x^2-1[\/latex]<\/li>\n \t
  13. [latex]x=\\dfrac{1}{5}, x=-\\dfrac{1}{5}[\/latex]\n[latex]x-\\dfrac{1}{5}=0, x+\\dfrac{1}{5}=0[\/latex][latex]0=(x-\\dfrac{1}{5})(x+\\dfrac{1}{5}) [\/latex]\n[latex]0=x^2-\\dfrac{1}{25}[\/latex]<\/li>\n \t
  14. [latex]x=\\sqrt{7}, x=-\\sqrt{7}[\/latex]\n[latex]x-\\sqrt{7}=0, x+\\sqrt{7}=0[\/latex][latex]0=(x-\\sqrt{7})(x+\\sqrt{7})[\/latex]\n[latex]0=x^2-7[\/latex]<\/li>\n \t
  15. [latex]x=\\sqrt{11}, x=-\\sqrt{11}[\/latex]\n[latex]x-\\sqrt{11}=0, x+\\sqrt{11}=0[\/latex][latex]0=(x-\\sqrt{11})(x+\\sqrt{11})[\/latex]\n[latex]0=x^2-11[\/latex]<\/li>\n \t
  16. [latex]x=2\\sqrt{3}, x=-2\\sqrt{3}[\/latex]\n[latex]x-2\\sqrt{3}=0, x+2\\sqrt{3}=0[\/latex][latex]0=(x-2\\sqrt{3})(x+2\\sqrt{3})[\/latex]\n[latex]0=x^2-12[\/latex]<\/li>\n \t
  17. [latex]x=3, x=5, x=8[\/latex]\n[latex](x-3)=0, (x-5)=0, (x-8)=0[\/latex][latex]\\begin{array}{rrcrcrrrr}\n(x&-&3)(x&-&5)(x&-&8)&=&0 \\\\\n(x^2&-&8x&+&15)(x&-&8)&=&0 \\\\\nx^3&-&8x^2&+&15x&&&& \\\\\n&-&8x^2&+&64x&-&120&=&0 \\\\\n\\hline\nx^3&-&16x^2&+&79x&-&120&=&0\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]x=-4, x=0, x=4[\/latex]\n[latex]x+4=0, x, x-4=0[\/latex][latex]x(x+4)(x-4)=0[\/latex]\n[latex]x(x^2-16)=0[\/latex]\n[latex]x^3-16x=0[\/latex]<\/li>\n \t
  19. [latex]x=-9, x+6=0, x=-2[\/latex]\n[latex]x+9=0, x+6=0, x+2=0[\/latex][latex]\\begin{array}{rrcrcrrrr}\n(x&+&9)(x&+&6)(x&+&2)&=&0 \\\\\n(x^2&+&15x&+&54)(x&+&2)&=&0 \\\\\nx^3&+&15x^2&+&54x&&&& \\\\\n&+&2x^2&+&30x&+&108&=&0 \\\\\n\\hline\nx^3&+&17x^2&+&84x&+&108&=&0\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]x=-1, x=1, x=5[\/latex]\n[latex]x+1=0, x-1=0, x-5=0[\/latex][latex](x+1)(x-1)(x-5)=0[\/latex]\n[latex](x^2-1)(x-5)=0[\/latex]\n[latex]x^3-5x^2-x+5=0[\/latex]<\/li>\n \t
  21. [latex]x=-2, x=2, x=5, x=-5[\/latex]\n[latex]x+2=0, x-2=0, x-5=0, x+5=0[\/latex][latex](x+2)(x-2)(x-5)(x+5)=0[\/latex]\n[latex](x^2-4)(x^2-25)=0[\/latex]\n[latex]x^4-29x^2+100=0[\/latex]<\/li>\n \t
  22. [latex]x=2\\sqrt{3}, x=-2\\sqrt{3}, x=\\sqrt{5}, x=-\\sqrt{5}[\/latex]\n[latex]x-2\\sqrt{3}=0, x+2\\sqrt{3}=0, x-\\sqrt{5}=0, x+\\sqrt{5}=0[\/latex][latex](x-2\\sqrt{3})(x+2\\sqrt{3})(x-\\sqrt{5})(x+\\sqrt{5})=0[\/latex]\n[latex](x^2-12)(x^2-5)=0[\/latex]\n[latex]x^4-17x^2+60=0[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]x=5, x=2[\/latex]
      \n[latex]x-5=0, x-2=0[\/latex][latex]0=(x-5)(x-2)[\/latex]
      \n[latex]0=x^2-7x+10[\/latex]<\/li>\n
    2. [latex]x=3, x=6[\/latex]
      \n[latex]x-3=0, x-6=0[\/latex][latex](x-3)(x-6)=0[\/latex]
      \n[latex]0=x^2-9x+18[\/latex]<\/li>\n
    3. [latex]x=20, x=2[\/latex]
      \n[latex]x-20=0, x-2=0[\/latex][latex]0=(x-20)(x-2)[\/latex]
      \n[latex]0=x^2-22x+40[\/latex]<\/li>\n
    4. [latex]x=13, x=1[\/latex]
      \n[latex]x-13=0, x-1=0[\/latex][latex]0=(x-13)(x-1)[\/latex]
      \n[latex]0=x^2-14x+13[\/latex]<\/li>\n
    5. [latex]x=4, x=4[\/latex]
      \n[latex]x-4=0, x-4=0[\/latex][latex]0=(x-4)(x-4)[\/latex]
      \n[latex]0=x^2-8x+16[\/latex]<\/li>\n
    6. [latex]x=0, x=9[\/latex]
      \n[latex]x-9=0, x[\/latex][latex]x(x-9)=0[\/latex]
      \n[latex]0=x^2-9x[\/latex]<\/li>\n
    7. [latex]x=\\dfrac{3}{4}, x=\\dfrac{1}{4}[\/latex]
      \n[latex]x-\\dfrac{3}{4}=0, x-\\dfrac{1}{4}=0[\/latex][latex]0=\\left(x-\\dfrac{3}{4}\\right)\\left(x-\\dfrac{1}{4}\\right)[\/latex]
      \n[latex]0=x^2-x+\\dfrac{3}{16}[\/latex]<\/li>\n
    8. [latex]x=\\dfrac{5}{8}, x=\\dfrac{5}{7}[\/latex]
      \n[latex]x-\\dfrac{5}{8}=0, x-\\dfrac{5}{7}=0[\/latex][latex]0=\\left(x-\\dfrac{5}{8}\\right)\\left(x-\\dfrac{5}{7}\\right)[\/latex]
      \n[latex]0=x^2-\\dfrac{75}{56}x+\\dfrac{25}{56}[\/latex]<\/li>\n
    9. [latex]x=\\dfrac{1}{2}, x=\\dfrac{1}{3}[\/latex]
      \n[latex]x-\\dfrac{1}{2}=0, x-\\dfrac{1}{3}=0[\/latex][latex]0=\\left(x-\\dfrac{1}{2}\\right)\\left(x-\\dfrac{1}{3}\\right)[\/latex]
      \n[latex]0=x^2-\\dfrac{5}{6}x+\\dfrac{1}{6}[\/latex]<\/li>\n
    10. [latex]x=\\dfrac{1}{2}, x=\\dfrac{2}{3}[\/latex]
      \n[latex]x-\\dfrac{1}{2}=0, x-\\dfrac{2}{3}=0[\/latex][latex]0=\\left(x-\\dfrac{1}{2}\\right)\\left(x-\\dfrac{2}{3}\\right)[\/latex]
      \n[latex]0=x^2-\\dfrac{7}{6}x+\\dfrac{1}{3}[\/latex]<\/li>\n
    11. [latex]x=5, x=-5[\/latex]
      \n[latex]x-5=0, x+5=0[\/latex][latex]0=(x-5)(x+5)[\/latex]
      \n[latex]0=x^2-25[\/latex]<\/li>\n
    12. [latex]x=1, x=-1[\/latex]
      \n[latex]x-1=0, x+1=0[\/latex][latex]0=(x-1)(x+1)[\/latex]
      \n[latex]0=x^2-1[\/latex]<\/li>\n
    13. [latex]x=\\dfrac{1}{5}, x=-\\dfrac{1}{5}[\/latex]
      \n[latex]x-\\dfrac{1}{5}=0, x+\\dfrac{1}{5}=0[\/latex][latex]0=(x-\\dfrac{1}{5})(x+\\dfrac{1}{5})[\/latex]
      \n[latex]0=x^2-\\dfrac{1}{25}[\/latex]<\/li>\n
    14. [latex]x=\\sqrt{7}, x=-\\sqrt{7}[\/latex]
      \n[latex]x-\\sqrt{7}=0, x+\\sqrt{7}=0[\/latex][latex]0=(x-\\sqrt{7})(x+\\sqrt{7})[\/latex]
      \n[latex]0=x^2-7[\/latex]<\/li>\n
    15. [latex]x=\\sqrt{11}, x=-\\sqrt{11}[\/latex]
      \n[latex]x-\\sqrt{11}=0, x+\\sqrt{11}=0[\/latex][latex]0=(x-\\sqrt{11})(x+\\sqrt{11})[\/latex]
      \n[latex]0=x^2-11[\/latex]<\/li>\n
    16. [latex]x=2\\sqrt{3}, x=-2\\sqrt{3}[\/latex]
      \n[latex]x-2\\sqrt{3}=0, x+2\\sqrt{3}=0[\/latex][latex]0=(x-2\\sqrt{3})(x+2\\sqrt{3})[\/latex]
      \n[latex]0=x^2-12[\/latex]<\/li>\n
    17. [latex]x=3, x=5, x=8[\/latex]
      \n[latex](x-3)=0, (x-5)=0, (x-8)=0[\/latex][latex]\\begin{array}{rrcrcrrrr} (x&-&3)(x&-&5)(x&-&8)&=&0 \\\\ (x^2&-&8x&+&15)(x&-&8)&=&0 \\\\ x^3&-&8x^2&+&15x&&&& \\\\ &-&8x^2&+&64x&-&120&=&0 \\\\ \\hline x^3&-&16x^2&+&79x&-&120&=&0 \\end{array}[\/latex]<\/li>\n
    18. [latex]x=-4, x=0, x=4[\/latex]
      \n[latex]x+4=0, x, x-4=0[\/latex][latex]x(x+4)(x-4)=0[\/latex]
      \n[latex]x(x^2-16)=0[\/latex]
      \n[latex]x^3-16x=0[\/latex]<\/li>\n
    19. [latex]x=-9, x+6=0, x=-2[\/latex]
      \n[latex]x+9=0, x+6=0, x+2=0[\/latex][latex]\\begin{array}{rrcrcrrrr} (x&+&9)(x&+&6)(x&+&2)&=&0 \\\\ (x^2&+&15x&+&54)(x&+&2)&=&0 \\\\ x^3&+&15x^2&+&54x&&&& \\\\ &+&2x^2&+&30x&+&108&=&0 \\\\ \\hline x^3&+&17x^2&+&84x&+&108&=&0 \\end{array}[\/latex]<\/li>\n
    20. [latex]x=-1, x=1, x=5[\/latex]
      \n[latex]x+1=0, x-1=0, x-5=0[\/latex][latex](x+1)(x-1)(x-5)=0[\/latex]
      \n[latex](x^2-1)(x-5)=0[\/latex]
      \n[latex]x^3-5x^2-x+5=0[\/latex]<\/li>\n
    21. [latex]x=-2, x=2, x=5, x=-5[\/latex]
      \n[latex]x+2=0, x-2=0, x-5=0, x+5=0[\/latex][latex](x+2)(x-2)(x-5)(x+5)=0[\/latex]
      \n[latex](x^2-4)(x^2-25)=0[\/latex]
      \n[latex]x^4-29x^2+100=0[\/latex]<\/li>\n
    22. [latex]x=2\\sqrt{3}, x=-2\\sqrt{3}, x=\\sqrt{5}, x=-\\sqrt{5}[\/latex]
      \n[latex]x-2\\sqrt{3}=0, x+2\\sqrt{3}=0, x-\\sqrt{5}=0, x+\\sqrt{5}=0[\/latex][latex](x-2\\sqrt{3})(x+2\\sqrt{3})(x-\\sqrt{5})(x+\\sqrt{5})=0[\/latex]
      \n[latex](x^2-12)(x^2-5)=0[\/latex]
      \n[latex]x^4-17x^2+60=0[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":100,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2002","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2002","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2002\/revisions"}],"predecessor-version":[{"id":2003,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2002\/revisions\/2003"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2002\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2002"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2002"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2002"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}