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Given p(x) = x4 – 13x2 – 25x – 12.

A) Use long division to determine the remainder when p(x) is divided by (x2 – 4)? Show all of your work for full credit.

B) Use mathematical methods to prove that your quotient and remainder are correct. Show all of your work for full credit.

Respuesta :

Answer:

Below.

Step-by-step explanation:

p(x) = x^4 - 13x^2 – 25x – 12

Long division:

x^2 - 4)x^4 - 13x^2 – 25x – 12( x^2 - 9  <-------- Quotient

           x^4 -  4x^2

Subtract:       -9x^2 -  25x

                     -9x^2  + 36

                                 -25x - 36 - 12

So the remainder is -25x - 48 (Answer).

B)   If the above are correct then:

(x^2 - 4) * quotient + remainder  = the original form of  p(x).

(x^2 - 4)(x^2 -9)  - 25x - 48 = the original p(x).

p(x) = x^4 - 9x^2 - 4x^2 + 36  - 25x - 48

= x^4 - 13x^2 - 25x -12 = original p(x)

                   

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