Example Question 4

Example corresponding to question 4 in college algebra 2.

Example 1


Which of the following polynomial equations has the solution set {-5,-3,-1,0,3}?

  1. $(x-5)(x-1)(x^2+9)=0$


  2. $(x+5)(x+1)(x^2+9)=0$


  3. $x(x-5)(x-1)(x^2+9)=0$


  4. $(x+5)(x+1)(x^2-9)=0$


  5. $x(x+5)(x+1)(x^2-9)=0$

Solution


  1. We first start by writing a polynomial as a product of linear factors using the given solution set as follows

    $(x+5)(x+3)(x+1)(x-0)(x-3)$

  2. Note that $(x-3)(x+3) = x^2-9$, hence the equation with the given solutions may be given as follows

    $x(x+5)(x+1)(x^2-9)=0$

    Answer E