(a⁴-19a²+9)/(a²-5a+3)= ??? Answer = a²+5a+3

2 Answers
Ratnaker Mehta
Sep 14, 2017

Kindly refer to the Explanation.

Explanation:

To complete the Square #a^4+9,# we require, as the Middle Term,

#pm6a^2.#

We select #+6a^2,# and find,

#a^4-19a^2+9,#

#=ul(a^4+6a^2+9)-25a^2,#

#=(a^2+3)^3-(5a)^2,#

#:. (a^4-19a^2+9)=(a^2-5a+3)(a^2+5a+3).......(star).#

Hence, we have, #(a^4-19a^2+9)/((a^2-5a+3),#

#={cancel((a^2-5a+3))(a^2+5a+3)}/cancel((a^2-5a+3))........[because, (star)],#

#=a^2+5a+3#.

Jim G.
Sep 14, 2017

#a^2+5a+3#

Explanation:

#"one way to divide is to use the divisor as a factor in the"#
#"numerator"#

#"consider the numerator"#

#a^2(a^2-5a+3)+5a(a^2-5a+3)+3(a^2-5a+3)+0#

#rArr(a^4-19a^2+9)/(a^2-5a+3)#

#=(cancel((a^2-5a+3))(a^2+5a+3))/cancel((a^2-5a+3))=a^2+5a+3#

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