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What is the answer for question 2) ? http://postimg.org/image/rrpvfng7p/ (Reminder) :...

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jayson94 | (Level 1) Salutatorian

Posted August 2, 2013 at 11:22 AM via web

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What is the answer for question 2) ?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted August 2, 2013 at 12:33 PM (Answer #1)

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(a) If the divisor is a factor the remainder will be zero.

(b)          x   +   a
              ---------
     x-a   | `x^2-a^2`
               `x^2-ax`
               -----------
                     `ax-a^2`
                     `ax-a^2`
                     ---------
                            0

(c)            `x^2+ax+a^2`
               -----------------
      x-a   | `x^3`                 `-a^3`
                `x^3-ax^2`
               ------------
                    `ax^2`
                    `ax^2-a^2x`
                   ---------------
                             `a^2x-a^3`
                             `a^2x-a^3`
                              ------------
                                      0

(d)           `x^3+ax^2+a^2x+a^3`
               ----------------------------
         x-a |`x^4`                             `-a^4`
                `x^4-ax^3`
                -----------
                      `ax^3`
                      `ax^3-a^2x^2`
                      ---------------
                                 `a^2x^2`
                                 `a^2x^2-a^3x`
                                 ---------------
                                           `a^3x-a^4`
                                           `a^3x-a^4`
                                          ------------
                                                   0

(e) Try x+a as a factor:

           `x^2-ax+a^2`
           ------------------
 x+a   | `x^3`                  `+a^3`
           `x^3+ax^2`
          ------------
                 `-ax^2`
                 `-ax^2-a^2x`
                 ----------------
                            `a^2x+a^3`
                            `a^2x+a^3`
                            --------------
                                  0

(f) Neither x+a or x-a is a factor.

The sum of two squares does not factor in the real numbers.

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