{"id":1901,"date":"2021-12-02T19:39:54","date_gmt":"2021-12-03T00:39:54","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-4\/"},"modified":"2023-09-01T14:16:37","modified_gmt":"2023-09-01T18:16:37","slug":"answer-key-7-4","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-4\/","title":{"raw":"Answer Key 7.4","rendered":"Answer Key 7.4"},"content":{"raw":"
    \r\n \t
  1. [latex]-21\\times 2=-42[\/latex]\r\n[latex]-21+2=-19[\/latex]\r\n[latex]7x^2-21x+2x-6[\/latex]\r\n[latex]7x(x-3)+2(x-3)[\/latex]\r\n[latex](x-3)(7x+2)[\/latex]<\/li>\r\n \t
  2. [latex]-6\\times 4=-24[\/latex]\r\n[latex]-6+4=-2[\/latex]\r\n[latex]3n^2-6n+4n-8[\/latex]\r\n[latex]3n(n-2)+4(n-2)[\/latex]\r\n[latex](n-2)(3n+4)[\/latex]<\/li>\r\n \t
  3. [latex]14\\times 1=14[\/latex]\r\n[latex]14+1=15[\/latex]\r\n[latex]7b^2+14b+b+2[\/latex]\r\n[latex]7b(b+2)+1(b+2)[\/latex]\r\n[latex](b+2)(7b+1)[\/latex]<\/li>\r\n \t
  4. [latex]-14\\times 3=-42[\/latex]\r\n[latex]-14+3=-11[\/latex]\r\n[latex]21v^2-14v+3v-2[\/latex]\r\n[latex]7v(3v-2)+1(3v-2)[\/latex]\r\n[latex](3v-2)(7v+1)[\/latex]<\/li>\r\n \t
  5. [latex]15\\times -2=-30[\/latex]\r\n[latex]15+-2=13[\/latex]\r\n[latex]5a^2+15a-2a-6[\/latex]\r\n[latex]5a(a+3)-2(a+3)[\/latex]\r\n[latex](a+3)(5a-2)[\/latex]<\/li>\r\n \t
  6. [latex]-20\\times 2=-40[\/latex]\r\n[latex]-20+2=-18[\/latex]\r\n[latex]5n^2-20n+2n-8[\/latex]\r\n[latex]5n(n-4)+2(n-4)[\/latex]\r\n[latex](n-4)(5n+2)[\/latex]<\/li>\r\n \t
  7. [latex]-1\\times -4=4[\/latex]\r\n[latex]-1+-4=-5[\/latex]\r\n[latex]2x^2-x-4x+2[\/latex]\r\n[latex]x(2x-1)-2(2x-1)[\/latex]\r\n[latex](2x-1)(x-2)[\/latex]<\/li>\r\n \t
  8. [latex]-6\\times 2=-12[\/latex]\r\n[latex]-6+2=-4[\/latex]\r\n[latex]3r^2-6r+2r-4[\/latex]\r\n[latex]3r(r-2)+2(r-2)[\/latex]\r\n[latex](r-2)(3r+2)[\/latex]<\/li>\r\n \t
  9. [latex]14\\times 5=70[\/latex]\r\n[latex]14+5=19[\/latex]\r\n[latex]2x^2+14x+5x+35[\/latex]\r\n[latex]2x(x+7)+5(x+7)[\/latex]\r\n[latex](x+7)(2x+5)[\/latex]<\/li>\r\n \t
  10. [latex]9\\times -5=-45[\/latex]\r\n[latex]9+-5=4[\/latex]\r\n[latex]3x^2+9x-5x-15[\/latex]\r\n[latex]3x(x+3)-5(x+3)[\/latex]\r\n[latex](x+3)(3x-5)[\/latex]<\/li>\r\n \t
  11. [latex]-3\\times 2=-6[\/latex]\r\n[latex]-3+2=-1[\/latex]\r\n[latex]2b^2-3b+2b-3[\/latex]\r\n[latex]b(2b-3)+1(2b-3)[\/latex]\r\n[latex](2b-3)(b+1)[\/latex]<\/li>\r\n \t
  12. [latex]8\\times -3=-24[\/latex]\r\n[latex]8+-3=5[\/latex]\r\n[latex]2k^2+8k-3k-12[\/latex]\r\n[latex]2k(k+4)-3(k+4)[\/latex]\r\n[latex](k+4)(2k-3)[\/latex]<\/li>\r\n \t
  13. [latex]15\\times 2=30[\/latex]\r\n[latex]15+2=17[\/latex]\r\n[latex]3x^2+15xy+2xy+10y^2[\/latex]\r\n[latex]3x(x+5y)+2y(x+5y)[\/latex]\r\n[latex](x+5y)(3x+2y)[\/latex]<\/li>\r\n \t
  14. [latex]-7\\times 5=-35[\/latex]\r\n[latex]-7+5=-2[\/latex]\r\n[latex]7x^2-7xy+5xy-5y^2[\/latex]\r\n[latex]7x(x-y)+5y(x-y)[\/latex]\r\n[latex](x-y)(7x+5y)[\/latex]<\/li>\r\n \t
  15. [latex]15\\times -4=-60[\/latex]\r\n[latex]15+-4=11[\/latex]\r\n[latex]3x^2+15xy-4xy-20y^2[\/latex]\r\n[latex]3x(x+5y)-4y(x+5y)[\/latex]\r\n[latex](x+5y)(3x-4y)[\/latex]<\/li>\r\n \t
  16. [latex]18\\times -2=-36[\/latex]\r\n[latex]18+-2=16[\/latex]\r\n[latex]12u^2+18uv-2uv-3v^2[\/latex]\r\n[latex]6u(2u+3v)-v(2u+3v)[\/latex]\r\n[latex](2u+3v)(6u-v)[\/latex]<\/li>\r\n \t
  17. [latex]-16\\times -1=16[\/latex]\r\n[latex]-16+-1=-17[\/latex]\r\n[latex]4k^2-16k-k+4[\/latex]\r\n[latex]4k(k-4)-1(k-4)[\/latex]\r\n[latex](k-4)(4k-1)[\/latex]<\/li>\r\n \t
  18. [latex]7\\times -4=-28[\/latex]\r\n[latex]7+-4=3[\/latex]\r\n[latex]4r^2+7r-4r-7[\/latex]\r\n[latex]r(4r+7)-1(4r+7)[\/latex]\r\n[latex](4r+7)(r-1)[\/latex]<\/li>\r\n \t
  19. [latex]-12\\times 3=-36[\/latex]\r\n[latex]-12+3=-9[\/latex]\r\n[latex]4m^2-12mn+3mn-9n^2[\/latex]\r\n[latex]4m(m-3n)+3n(m-3n)[\/latex]\r\n[latex](m-3n)(4m+3n)[\/latex]<\/li>\r\n \t
  20. [latex]\\text{Cannot be factored.}[\/latex]<\/li>\r\n \t
  21. [latex]12\\times 1=12[\/latex]\r\n[latex]12+1=13[\/latex]\r\n[latex]4x^2+12xy+xy+3y^2[\/latex]\r\n[latex]4x(x+3y)+y(x+3y)[\/latex]\r\n[latex](x+3y)(4x+y)[\/latex]<\/li>\r\n \t
  22. [latex]8\\times -3=-24[\/latex]\r\n[latex]8+-3=5[\/latex]\r\n[latex]6u^2+8uv-3uv-4v^2[\/latex]\r\n[latex]2u(3u+4v)-v(3u+4v)[\/latex]\r\n[latex](3u+4v)(2u-v)[\/latex]<\/li>\r\n \t
  23. [latex]20\\times -1=-20[\/latex]\r\n[latex]20+-1=19[\/latex]\r\n[latex]10x^2+20xy-xy-2y^2[\/latex]\r\n[latex]10x(x+2y)-1(x+2y)[\/latex]\r\n[latex](x-2y)(10x-y)[\/latex]<\/li>\r\n \t
  24. [latex]-15\\times 2=-30[\/latex]\r\n[latex]-15+2=-13[\/latex]\r\n[latex]6x^2-15xy+2xy-5y^2[\/latex]\r\n[latex]3x(2x-5y)+y(2x-5y)[\/latex]\r\n[latex](2x-5y)(3x+y)[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]-21\\times 2=-42[\/latex]
      \n[latex]-21+2=-19[\/latex]
      \n[latex]7x^2-21x+2x-6[\/latex]
      \n[latex]7x(x-3)+2(x-3)[\/latex]
      \n[latex](x-3)(7x+2)[\/latex]<\/li>\n
    2. [latex]-6\\times 4=-24[\/latex]
      \n[latex]-6+4=-2[\/latex]
      \n[latex]3n^2-6n+4n-8[\/latex]
      \n[latex]3n(n-2)+4(n-2)[\/latex]
      \n[latex](n-2)(3n+4)[\/latex]<\/li>\n
    3. [latex]14\\times 1=14[\/latex]
      \n[latex]14+1=15[\/latex]
      \n[latex]7b^2+14b+b+2[\/latex]
      \n[latex]7b(b+2)+1(b+2)[\/latex]
      \n[latex](b+2)(7b+1)[\/latex]<\/li>\n
    4. [latex]-14\\times 3=-42[\/latex]
      \n[latex]-14+3=-11[\/latex]
      \n[latex]21v^2-14v+3v-2[\/latex]
      \n[latex]7v(3v-2)+1(3v-2)[\/latex]
      \n[latex](3v-2)(7v+1)[\/latex]<\/li>\n
    5. [latex]15\\times -2=-30[\/latex]
      \n[latex]15+-2=13[\/latex]
      \n[latex]5a^2+15a-2a-6[\/latex]
      \n[latex]5a(a+3)-2(a+3)[\/latex]
      \n[latex](a+3)(5a-2)[\/latex]<\/li>\n
    6. [latex]-20\\times 2=-40[\/latex]
      \n[latex]-20+2=-18[\/latex]
      \n[latex]5n^2-20n+2n-8[\/latex]
      \n[latex]5n(n-4)+2(n-4)[\/latex]
      \n[latex](n-4)(5n+2)[\/latex]<\/li>\n
    7. [latex]-1\\times -4=4[\/latex]
      \n[latex]-1+-4=-5[\/latex]
      \n[latex]2x^2-x-4x+2[\/latex]
      \n[latex]x(2x-1)-2(2x-1)[\/latex]
      \n[latex](2x-1)(x-2)[\/latex]<\/li>\n
    8. [latex]-6\\times 2=-12[\/latex]
      \n[latex]-6+2=-4[\/latex]
      \n[latex]3r^2-6r+2r-4[\/latex]
      \n[latex]3r(r-2)+2(r-2)[\/latex]
      \n[latex](r-2)(3r+2)[\/latex]<\/li>\n
    9. [latex]14\\times 5=70[\/latex]
      \n[latex]14+5=19[\/latex]
      \n[latex]2x^2+14x+5x+35[\/latex]
      \n[latex]2x(x+7)+5(x+7)[\/latex]
      \n[latex](x+7)(2x+5)[\/latex]<\/li>\n
    10. [latex]9\\times -5=-45[\/latex]
      \n[latex]9+-5=4[\/latex]
      \n[latex]3x^2+9x-5x-15[\/latex]
      \n[latex]3x(x+3)-5(x+3)[\/latex]
      \n[latex](x+3)(3x-5)[\/latex]<\/li>\n
    11. [latex]-3\\times 2=-6[\/latex]
      \n[latex]-3+2=-1[\/latex]
      \n[latex]2b^2-3b+2b-3[\/latex]
      \n[latex]b(2b-3)+1(2b-3)[\/latex]
      \n[latex](2b-3)(b+1)[\/latex]<\/li>\n
    12. [latex]8\\times -3=-24[\/latex]
      \n[latex]8+-3=5[\/latex]
      \n[latex]2k^2+8k-3k-12[\/latex]
      \n[latex]2k(k+4)-3(k+4)[\/latex]
      \n[latex](k+4)(2k-3)[\/latex]<\/li>\n
    13. [latex]15\\times 2=30[\/latex]
      \n[latex]15+2=17[\/latex]
      \n[latex]3x^2+15xy+2xy+10y^2[\/latex]
      \n[latex]3x(x+5y)+2y(x+5y)[\/latex]
      \n[latex](x+5y)(3x+2y)[\/latex]<\/li>\n
    14. [latex]-7\\times 5=-35[\/latex]
      \n[latex]-7+5=-2[\/latex]
      \n[latex]7x^2-7xy+5xy-5y^2[\/latex]
      \n[latex]7x(x-y)+5y(x-y)[\/latex]
      \n[latex](x-y)(7x+5y)[\/latex]<\/li>\n
    15. [latex]15\\times -4=-60[\/latex]
      \n[latex]15+-4=11[\/latex]
      \n[latex]3x^2+15xy-4xy-20y^2[\/latex]
      \n[latex]3x(x+5y)-4y(x+5y)[\/latex]
      \n[latex](x+5y)(3x-4y)[\/latex]<\/li>\n
    16. [latex]18\\times -2=-36[\/latex]
      \n[latex]18+-2=16[\/latex]
      \n[latex]12u^2+18uv-2uv-3v^2[\/latex]
      \n[latex]6u(2u+3v)-v(2u+3v)[\/latex]
      \n[latex](2u+3v)(6u-v)[\/latex]<\/li>\n
    17. [latex]-16\\times -1=16[\/latex]
      \n[latex]-16+-1=-17[\/latex]
      \n[latex]4k^2-16k-k+4[\/latex]
      \n[latex]4k(k-4)-1(k-4)[\/latex]
      \n[latex](k-4)(4k-1)[\/latex]<\/li>\n
    18. [latex]7\\times -4=-28[\/latex]
      \n[latex]7+-4=3[\/latex]
      \n[latex]4r^2+7r-4r-7[\/latex]
      \n[latex]r(4r+7)-1(4r+7)[\/latex]
      \n[latex](4r+7)(r-1)[\/latex]<\/li>\n
    19. [latex]-12\\times 3=-36[\/latex]
      \n[latex]-12+3=-9[\/latex]
      \n[latex]4m^2-12mn+3mn-9n^2[\/latex]
      \n[latex]4m(m-3n)+3n(m-3n)[\/latex]
      \n[latex](m-3n)(4m+3n)[\/latex]<\/li>\n
    20. [latex]\\text{Cannot be factored.}[\/latex]<\/li>\n
    21. [latex]12\\times 1=12[\/latex]
      \n[latex]12+1=13[\/latex]
      \n[latex]4x^2+12xy+xy+3y^2[\/latex]
      \n[latex]4x(x+3y)+y(x+3y)[\/latex]
      \n[latex](x+3y)(4x+y)[\/latex]<\/li>\n
    22. [latex]8\\times -3=-24[\/latex]
      \n[latex]8+-3=5[\/latex]
      \n[latex]6u^2+8uv-3uv-4v^2[\/latex]
      \n[latex]2u(3u+4v)-v(3u+4v)[\/latex]
      \n[latex](3u+4v)(2u-v)[\/latex]<\/li>\n
    23. [latex]20\\times -1=-20[\/latex]
      \n[latex]20+-1=19[\/latex]
      \n[latex]10x^2+20xy-xy-2y^2[\/latex]
      \n[latex]10x(x+2y)-1(x+2y)[\/latex]
      \n[latex](x-2y)(10x-y)[\/latex]<\/li>\n
    24. [latex]-15\\times 2=-30[\/latex]
      \n[latex]-15+2=-13[\/latex]
      \n[latex]6x^2-15xy+2xy-5y^2[\/latex]
      \n[latex]3x(2x-5y)+y(2x-5y)[\/latex]
      \n[latex](2x-5y)(3x+y)[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":61,"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-1901","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\/1901","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":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1901\/revisions"}],"predecessor-version":[{"id":2219,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1901\/revisions\/2219"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1901\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1901"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1901"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1901"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}