Question : What is the LCM of $\left(8 x^3+80 x^2+200 x\right)$ and $\left(4 x^4+16 x^3-20 x^2\right)$?
Option 1: $8 x^2(x+5)^2(x-1)$
Option 2: $8 x^2(x-1)^2(x+5)$
Option 3: $4 x^2(x-1)^2(x+5)$
Option 4: $4 x^2(x+5)^2(x-1)$
Correct Answer: $8 x^2(x+5)^2(x-1)$
Solution :
Consider, $(8 x^3+80 x^2+200 x)$
Taking $8x$ as common, we get,
$=8x(x^2+10x+25)$
$=8x(x^2+5x+5x+25)$
$=8x(x(x+5)+5(x+5))$
$=8x(x+5)^2$
Now consider, $(4 x^4+16 x^3-20 x^2)$
Taking $4x^2$ as common, we get,
$=4x^2(x^2 + 4x-5)$
$=4x^2(x^2-x+5x-5)$
$=4x^2(x(x-1)+5(x-1))$
$=4x^2(x-1)(x+5)$
$\therefore$ LCM $=8x^2(x+5)^2(x-1)$
Hence, the correct answer is $8x^2(x+5)^2(x-1)$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
