Answer Key 7.4

  1. -21\times 2=-42
    -21+2=-19
    7x^2-21x+2x-6
    7x(x-3)+2(x-3)
    (x-3)(7x+2)
  2. -6\times 4=-24
    -6+4=-2
    3n^2-6n+4n-8
    3n(n-2)+4(n-2)
    (n-2)(3n+4)
  3. 14\times 1=14
    14+1=15
    7b^2+14b+b+2
    7b(b+2)+1(b+2)
    (b+2)(7b+1)
  4. -14\times 3=-42
    -14+3=-11
    21v^2-14v+3v-2
    7v(3v-2)+1(3v-2)
    (3v-2)(7v+1)
  5. 15\times -2=-30
    15+-2=13
    5a^2+15a-2a-6
    5a(a+3)-2(a+3)
    (a+3)(5a-2)
  6. -20\times 2=-40
    -20+2=-18
    5n^2-20n+2n-8
    5n(n-4)+2(n-4)
    (n-4)(5n+2)
  7. -1\times -4=4
    -1+-4=-5
    2x^2-x-4x+2
    x(2x-1)-2(2x-1)
    (2x-1)(x-2)
  8. -6\times 2=-12
    -6+2=-4
    3r^2-6r+2r-4
    3r(r-2)+2(r-2)
    (r-2)(3r+2)
  9. 14\times 5=70
    14+5=19
    2x^2+14x+5x+35
    2x(x+7)+5(x+7)
    (x+7)(2x+5)
  10. 9\times -5=-45
    9+-5=4
    3x^2+9x-5x-15
    3x(x+3)-5(x+3)
    (x+3)(3x-5)
  11. -3\times 2=-6
    -3+2=-1
    2b^2-3b+2b-3
    b(2b-3)+1(2b-3)
    (2b-3)(b+1)
  12. 8\times -3=-24
    8+-3=5
    2k^2+8k-3k-12
    2k(k+4)-3(k+4)
    (k+4)(2k-3)
  13. 15\times 2=30
    15+2=17
    3x^2+15xy+2xy+10y^2
    3x(x+5y)+2y(x+5y)
    (x+5y)(3x+2y)
  14. -7\times 5=-35
    -7+5=-2
    7x^2-7xy+5xy-5y^2
    7x(x-y)+5y(x-y)
    (x-y)(7x+5y)
  15. 15\times -4=-60
    15+-4=11
    3x^2+15xy-4xy-20y^2
    3x(x+5y)-4y(x+5y)
    (x+5y)(3x-4y)
  16. 18\times -2=-36
    18+-2=16
    12u^2+18uv-2uv-3v^2
    6u(2u+3v)-v(2u+3v)
    (2u+3v)(6u-v)
  17. -16\times -1=16
    -16+-1=-17
    4k^2-16k-k+4
    4k(k-4)-1(k-4)
    (k-4)(4k-1)
  18. 7\times -4=-28
    7+-4=3
    4r^2+7r-4r-7
    r(4r+7)-1(4r+7)
    (4r+7)(r-1)
  19. -12\times 3=-36
    -12+3=-9
    4m^2-12mn+3mn-9n^2
    4m(m-3n)+3n(m-3n)
    (m-3n)(4m+3n)
  20. \text{Cannot be factored.}
  21. 12\times 1=12
    12+1=13
    4x^2+12xy+xy+3y^2
    4x(x+3y)+y(x+3y)
    (x+3y)(4x+y)
  22. 8\times -3=-24
    8+-3=5
    6u^2+8uv-3uv-4v^2
    2u(3u+4v)-v(3u+4v)
    (3u+4v)(2u-v)
  23. 20\times -1=-20
    20+-1=19
    10x^2+20xy-xy-2y^2
    10x(x+2y)-1(x+2y)
    (x-2y)(10x-y)
  24. -15\times 2=-30
    -15+2=-13
    6x^2-15xy+2xy-5y^2
    3x(2x-5y)+y(2x-5y)
    (2x-5y)(3x+y)

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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