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Midterm 3: Version D Answer Key

  1. 151m34n2⋅131n3453m6⋅31m43931n2⇒m12n151m34n2⋅131n3453m6⋅31m43931n2⇒m12n
  2. 3x2−9x3x+9⋅12xx2+2x−15⇒3x(x−3)3(x+3)⋅124x(x+5)(x−3)⇒12x2(x+3)(x+5)3x2−9x3x+9⋅12xx2+2x−15⇒3x(x−3)3(x+3)⋅124x(x+5)(x−3)⇒12x2(x+3)(x+5)
  3. (2x−4−6x−3=3)(x+4)(x−3)(2x−4−6x−3=3)(x+4)(x−3)
    2(x−3)−6(x+4)=3(x+4)(x−3)2x−6−6x−24=3(x2+x−12)−4x−30=3x2+3x−36+4x+30+4x+300=3x2+7x−60=(x+3)(3x−2)x=−3,232(x−3)−6(x+4)=3(x+4)(x−3)2x−6−6x−24=3(x2+x−12)−4x−30=3x2+3x−36+4x+30+4x+300=3x2+7x−60=(x+3)(3x−2)x=−3,23
  4. (x2y2−9)y3(x+3yy3)y3⇒x2y−9y3x+3y⇒y(x2−9y2)x+3y⇒y(x−3y)(x+3y)(x+3y)⇒y(x−3y)(x2y2−9)y3(x+3yy3)y3⇒x2y−9y3x+3y⇒y(x2−9y2)x+3y⇒y(x−3y)(x+3y)(x+3y)⇒y(x−3y)
  5. 5y2+2⋅7y+√25y2⋅y5y2+2⋅7y+√25y2⋅y
    5y2+14y+5y√y5y2+14y+5y√y
  6. 153−√5⋅3+√53+√5⇒45+15√59−5⇒45+15√54153−√5⋅3+√53+√5⇒45+15√59−5⇒45+15√54
  7. (a01b4c8d−12)14⇒b4⋅14c8⋅14d−12⋅14⇒bc2d−3⇒bd3c2(a01b4c8d−12)14⇒b4⋅14c8⋅14d−12⋅14⇒bc2d−3⇒bd3c2
  8. aa
    √2x+9−3=x+3x+3(√2x+9)2=(x+3)22x+9=x2+6x+9−2x−9−2x−90=x2+4x0=x(x+4)x=0,−4√2x+9−3=x+3x+3(√2x+9)2=(x+3)22x+9=x2+6x+9−2x−9−2x−90=x2+4x0=x(x+4)x=0,−4
  9. a
    1. 8x2−32x=08x(x−4)=0x=0,4
    2. 3x22=483√x2=√16x=±4
  10. a
    1. x2−5x+4=0(x−4)(x−1)=0x=1,4
    2. (x−3)(x−1)=0x=1,3
  11. a
    2(x+4)=x(x)2x+8=x20=x2−2x−80=x2−4x+2x−80=x(x−4)+2(x−4)0=(x−4)(x+2)x=−2,4
  12. a
    Let u=x2u2−48u−49=0(u−49)(u+1)=0(x2−49)(x2+1)=0(x−7)(x+7)(x2+1)=0x2+1=cannot be factoredx=±7
  13. a
    40=12(h−2)(h)80=h2−2h0=h2−2h−800=(h−10)(h+8)h=10,−8b=10−2=8
  14. x,x+2,x+4
    x(x+4)=41+4(x+2)x2+4x=41+4x+8−4x−4x√x2=√49x=±7
    numbers are 7,9,11 or −7,−5,−3
  15. a
    dd=du+42(6+r)=3(6−r)+412+2r=18−3r+4−12+3r−12+3r5r5=105r=2km/h

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