How do you factor by grouping $x^{3} + 6 x^{2} - 5 x - 30$ $x^3+6x^2-5x-30$ ?

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Answer 1 · 2015-06-08T19:03:13

$x^{3} + 6 x^{2} - 5 x - 30$ $x^3+6x^2-5x-30$

$= (x^{3} + 6 x^{2}) - (5 x + 30)$ $=(x^3+6x^2)-(5x+30)$

$= x^{2} \cdot (x + 6) - 5 \cdot (x + 6)$ $=x^2*(x+6)-5*(x+6)$

$= (x^{2} - 5) (x + 6)$ $=(x^2-5)(x+6)$

If you allow irrational coefficients...

$= (x^{2} - {(\sqrt{5})}^{2}) (x + 6)$ $=(x^2-(sqrt(5))^2)(x+6)$

$= (x - \sqrt{5}) (x + \sqrt{5}) (x + 6)$ $=(x-sqrt(5))(x+sqrt(5))(x+6)$

..using the difference of squares identity:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$

How do you factor by grouping x3+6x2−5x−30x^3+6x^2-5x-30?