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# How do you write y=x^3+6x^2-25x-150 in factored form?

Apr 21, 2018

$y = \left(x - 5\right) \left(x + 5\right) \left(x + 6\right)$

#### Explanation:

The difference of squares identity can be written:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

We will use this with $A = x$ and $B = 5$.

Given:

$y = {x}^{3} + 6 {x}^{2} - 25 x - 150$

Note that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic will factor by grouping:

$y = {x}^{3} + 6 {x}^{2} - 25 x - 150$

$\textcolor{w h i t e}{y} = \left({x}^{3} + 6 {x}^{2}\right) - \left(25 x + 150\right)$

$\textcolor{w h i t e}{y} = {x}^{2} \left(x + 6\right) - 25 \left(x + 6\right)$

$\textcolor{w h i t e}{y} = \left({x}^{2} - 25\right) \left(x + 6\right)$

$\textcolor{w h i t e}{y} = \left({x}^{2} - {5}^{2}\right) \left(x + 6\right)$

$\textcolor{w h i t e}{y} = \left(x - 5\right) \left(x + 5\right) \left(x + 6\right)$

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