For the fraction with numerator 8 x to the 7th power plus 10 x to the 6th power plus 20 x to the 5th power plus 33 x to the 4th power plus 23 x cubed plus 37 x squared plus 9 x plus 4 and denominator open paren x plus 1 close paren squared times open paren x squared plus 1 close paren cubed , which expression represents the correct form of the partial fraction decomposition?
Answer
A
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b squared and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c cubed and denominator open paren x plus 1 close paren cubed plus the fraction with numerator cap d x plus cap e and denominator x squared plus 1 plus the fraction with numerator open paren cap f x plus cap g close paren squared and denominator open paren x squared plus 1 close paren squared
B
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b squared and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c x plus cap d and denominator x squared plus 1 plus the fraction with numerator open paren cap e x plus cap f close paren squared and denominator open paren x squared plus 1 close paren squared plus the fraction with numerator open paren cap g x plus cap h close paren cubed and denominator open paren x squared plus 1 close paren cubed
C
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c and denominator open paren x plus 1 close paren cubed plus the fraction with numerator cap d x plus cap e and denominator x squared plus 1 plus the fraction with numerator cap f x plus cap g and denominator open paren x squared plus 1 close paren squared
D
the fraction with numerator cap A and denominator x plus 1 plus the fraction with numerator cap b and denominator open paren x plus 1 close paren squared plus the fraction with numerator cap c x plus cap d and denominator x squared plus 1 plus the fraction with numerator cap e x plus cap f and denominator open paren x squared plus 1 close paren squared plus the fraction with numerator cap g x plus cap h and denominator open paren x squared plus 1 close paren cubed