Factor Polynomial

Example on how to factor a polynomial with more than one variable .

Example 1

Factor a polynomial with more than one variable.
Factor completely $3 x y^3 + 6 x y^2 - 9 x y$

  1. $3(x y^3 + 2 x y^2 - 3 x y)$

  2. $3 x(y^3 + 2 y^2 - 3 y)$

  3. $3 x y(y^2 + 2 y - 3)$

  4. $3 x y(y-3)(y+1)$

  5. $3 x y (y+3)(y-1)$

Solution


  1. We first factor $3$ out

    $3 x y^3 + 6 x y^2 - 9 x y = 3(x y^3 + 2 x y^2 - 3 x y)$

  2. We next factor $x y$ out of the expression inside the parenthesis

    $=3 x y(y^2 + 2 y - 3)$

  3. We now factor the quadratic expression $y^2 + 2 y - 3$ to obtain complete factorization.

    $=3 x y(y - 3)( y+ 1)$

    Answer D