Question

eli uses the factor theorem to determine whether x−2 is a factor of 6x^5−22x^2 11x−126. how does he proceed to the correct answer?

Answer 1

Factor theorem states,

  "If a polynomial p(x) is divided by (x - a) and the remainder after the division is zero, (x - a) will be a factor of the polynomial."

   And we can represent it algebraically as,

   p(x) = (x - a)q(x)

   Here, q(x) is the quotient.

Now we will divide the given polynomial (6x⁵ - 22x² + 11x - 126) by (x - 2).

x - 2) 6x⁵ + 0.x⁴ + 0.x³ + 22x² + 11x - 126 (6x⁴+ 12x³+ 24x²+ 70x + 2

          6x⁵ - 12x⁴

         -------------------

                12x⁴ + 0.x³

                12x⁴ - 24x³

               --------------------

                           24x³ + 22x²                  

                           24x³ - 48x²

                         ---------------------------

                                      70x² + 11x

                                     70x² - 52x

                                --------------------------

                                                63x - 126

                                                63x - 126

                                              ------------------------

                                                           0

Since, remainder of the division is zero,

Therefore, (x - 2) is a factor of the given polynomial.

learn more of factor theorem here https://brainly.com/question/18575355

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