Online Course Discussion Forum

Math II-A homework question 4.22

 
 
Picture of Bober Yang
Math II-A homework question 4.22
by Bober Yang - Tuesday, 7 July 2020, 11:54 AM
 

so I was looking back at how the question is done then it said that 

 x4+7x3+14x2+7x+1
turns in to this:

x2(x2+2+1x2+7x+7+12)

I don't know how you do that because they are not equal

 
Picture of Areteem Professor
Re: Math II-A homework question 4.22
by Areteem Professor - Monday, 13 July 2020, 6:48 PM
 

Hi Bober, thanks for your patience.

There is indeed something missing in there. We should have $$x^2\left(x^2 + 2 + \dfrac{1}{x^2} + 7x  + \dfrac{7}{x} + 12\right).$$

Since $\left(x + \dfrac{1}{x}\right)^2 = x^2 + 2 + \frac{1}{x^2}$, we now have that the expression is equal to $x^2(y^2 + 7y + 12)$