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Math 51A Elementary Algebra - First Half

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  • Sample of what you should know before Math 51A:
     1. Factor:  28 y to the fourth minus 42 y cubed plus 35 y squared
      • Solution
        Since the greatest common factor is 7 y squared , we have:
        28 y to the fourth minus 42 y cubed plus 35 y squared
        7 y squared times open parenthesis 4 y squared minus 6 y plus 5 close parenthesis
     
    2. Solve:  11 n minus 4 times open parenthesis 2 n minus 3 close parenthesis equals 18 plus 5 times open parenthesis n plus 2 close parenthesis
     
    3. Subtract:  start fraction 1 over 2 t end fraction minus start fraction 3 over 5 t squared end fraction 
     
    4. Multiply, then combine like terms:  open parenthesis x plus 3 close parenthesis times open parenthesis 4 x squared minus 5 x plus 1 close parenthesis  

     

  • Sample of what you will learn in Math 51A:
     1. Solve:  3 times open parenthesis x squared plus 4 close parenthesis equals 20 x 
     
    2.  Factor completely:  24 a to the fourth plus 10 a cubed minus 4 a squared
     
    3.  Add:  start fractions 3 x minus 2 over x squared minus x minus 6 end fraction plus start fraction 4 x minus 3 over x squared minus 9 end fraction
      • Solution
        start fraction 3 x minus 2 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 2 close parenthesis end fraction plus start fraction 4 x minus 3 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis end fraction
        Since the least common denominator is open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis times open parenthesis x plus 2 close parenthesis, we have
        start fraction 3 x minus 2 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 2 close parenthesis end fraction times start fraction open parenthesis x plus 3 close parenthesis over open parenthesis x plus 3 close parenthesis end fraction = Start fraction 3 x squared plus 9 x minus 2 x minus 6 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis times open parenthesis x plus 2 close parenthesis end fraction
        Start fraction 4 x minus 3 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis end fraction times start fraction open parenthesis x plus 2 close parenthesis over open parenthesis x plus 2 close parenthesis end fraction = Start fraction 4 x squared plus 8 x minus 3 x minus 6 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis times open parenthesis x plus 2 close parenthesis end fraction
        equals start fraction 7 x squared plus 12 x minus 12 over open parenthesis x minus 3 close parenthesis times open parenthesis x plus 3 close parenthesis times open parenthesis x plus 2 close parenthesis end fraction