# Show that this quadratic factors to P = -5(x-9)(x-3).A company named Music Madness is a company that makes CD players. Last year, accountants modeled the company's profit by P= -5x^2+60x-135....

Show that this quadratic factors to P = -5(x-9)(x-3).

**A company named Music Madness is a company that makes CD players. Last year, accountants modeled the company's profit by P= -5x^2+60x-135.**

**Please explain fully how to answer this question. Thank you.**

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### 1 Answer

`P = -5x^2+60x-135`

Get (-5) out as a factor from the left side.

`P = (-5)((-5x^2)/(-5)+(60x)/(-5)-135/(-5))`

P = -5(x^2-**12**x+**27**) ----(1)

Now you should find two numbers which gives its addition as -12 and product as 27.

Addition -12 means the number before x in (1)

Product 27 means the number without x terms in (1)

`27 = 9xx3` which gives addition 9+3 = 12

`27 = (-9)xx(-3)` which gives addition (-9)+(-3) = -12

So the to numbers are (-9) and (-3).

Now e should rearrange (1) as the following.

P = -5(x^2-**12**x+27)

P = -5(x^2**-9x-3x**+27)

Now consider only the bracket.

**x^2-9x***-3x+27*

= **x(x-9)**-*3(x-9) *

you can see above in the first line x is common for the bold part and -3 is common for the italic part.

Then you will see (x-9) is common again for the second line.

**x^2-9x***-3x+27*

= **x(x-9)**-*3(x-9) *

= (x-9)(x-3)

So bracket can be rewritten as ;

`x^2-9x-3x+27 = (x-9)(x-3)`

P = -5(x^2-9x-3x+27)

*P = -5(x-9)(x-3)*

*So this is the answer what we want.*

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