Question

Find the quotient of 48a^4-16a^2-32/8a^2-8

Answer 1

we know that if we had
8/6=2/2 times 4/3=1 times 4/3=4/3
find common factors in top and obttom
factor
48a^4-16a^2-32=(16)(a-1)(a+1)(3a^2+2)
8a^2-8=8(a-1)(a+1)
so we have

`(48a^4-16a^2-32)/(8a^2-8) = ((2)(8)(a-1)(a+1)(3a^2+2))/((8)(a-1)(a+1))= ((8)/(8)) ((a-1)/(a-1))( (a+1)/(a+1)) ( ((2)(3a^(2)+2))/(1))=`(2)(3a^2+2)=6a^2+4


answer is 6a^2+4