How do you factor $y = x^{3} - x^{2} - 4 x + 4$ $y=x^3-x^2-4x+4$ ?

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Answer 1 · 2015-12-13T19:26:06

$y = (x - 2) (x + 2) (x - 1)$ $y= (x-2)(x+2)(x-1)$

Set the equation equal to zero

$x^{3} - x^{2} - 4 x + 4 = y$ $x^3 -x^2 -4x + 4 = y$

Group

$(x^{3} - x^{2}) + (- 4 x + 4) = y$ $(x^3-x^2 ) + (-4x +4) = y$

Factor the greatest common from each group

$\Rightarrow x^{2} (x - 1) - 4 (x - 1) = y$ $=>x^2(x-1) -4(x-1)= y$

Factor out the greatest common factor from the expression

$\Rightarrow (x^{2} - 4) (x - 1) = y$ $=>(x^2-4)(x-1) = y$

Factor the difference of square $(a^{2} - b^{2} = (a - b) (a + b)$ $(a^2-b^2 = (a-b)(a+b)$

$\Rightarrow (x - 2) (x + 2) (x - 1) = y$ $=>(x-2)(x+2)(x-1)= y$

How do you factor y=x^3-x^2-4x+4 y=x3−x2−4x+4y=x^3-x^2-4x+4 ?