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.

Expert Answers

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`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^2-12x+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^2-12x+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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