Help with Polynomial's (1 Viewer)

[markclyon]

Can anyone help with the following question.

Question

A monic polynomial P(x) of degree 4 is know to have single roots x=2 x=-2.

a) Write down an expression for P(x) to the extent specified.

b) If further, P(0)=4 and the division of P(x) by x-1 gives a remainder of 3, find P(x) in standard polynomial form.


Regards,

Mark.

 

[annabackwards]

a/ p(x) = (x-2)(x+2)(x-a)(x-b) where a and b are intergrals and cannot equal +/- 2

b/ p(0) = (-2)(2)(-a)(-b) = 4 so we get ab = -1
p(1) = (1-2)(1+2)(1-a)(1-b) = 3 so we get -3(1-a)(1-b) = 3 --> (1-a)(1-b) = -1

Then just solve simulatenously