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Math 51 Elementary Algebra

  • If you are considering taking a lower-level class than Math 51:
    • We encourage you to consider taking the corequisite courseMath 5—which provides additional support for Math 51.
    • The next level lower is Math 50 (Pre-Algebra).
  • If you are considering taking a higher-level class than Math 51:
 
  • Sample of what you should know before taking Math 51:
     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 
      • Solution
                  start fraction 1 times 5 t over 2 t times 5 t end fraction equals start fraction 5 t over 10 t squared end fraction
        minus start fraction 3 times 2 over 5 t squared times 2 end fraction equals start fraction 6 over 10 t squared end fraction
                                    start fraction 5 t minus 6 over 10 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 51:
     1. Solve:  3 times open parenthesis x squared plus 4 close parenthesis equals 20 x 
     2.  Factor:  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
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                                                              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
     4. Add or subtract wherever possible: 4 times start square root 3 end square root plus 2 times start square root 27 end square root minus 2 times start square root 12 end square root