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Example 1
Factor a polynomial with more than one variable.
Factor completely $3 x y^3 + 6 x y^2 - 9 x y$
- $3(x y^3 + 2 x y^2 - 3 x y)$
- $3 x(y^3 + 2 y^2 - 3 y)$
- $3 x y(y^2 + 2 y - 3)$
- $3 x y(y-3)(y+1)$
- $3 x y (y+3)(y-1)$
Solution
- We first factor $3$ out
$3 x y^3 + 6 x y^2 - 9 x y = 3(x y^3 + 2 x y^2 - 3 x y)$
- We next factor $x y$ out of the expression inside the parenthesis
$=3 x y(y^2 + 2 y - 3)$
- We now factor the quadratic expression $y^2 + 2 y - 3$ to obtain complete factorization.
$=3 x y(y - 3)( y+ 1)$
Answer D
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