Question

$\text{The LCM of}(x-3{)}^2(x+4\left)\text{and}\right(x-3\left)\right(x+4{)}^2\text{is}:$

• A. $(x-3{)}^2(x+4{)}^2$
• B. $(x-3)(x+4{)}^2$
• C. $(x-3{)}^2(x+4)$
• D. $(x-3)(x+4)$

Answer 1

The correct option is A $(x-3{)}^2(x+4{)}^2$

The irreducible factors occuring in $(x-3{)}^2(x+4\left)and\right(x-3\left)\right(x+4{)}^2$ are $(x-3)and(x+4)$
The greatest exponents of these factors respectively are 2 and 2.
Hence, the LCM = $(x-3{)}^2\times (x+4{)}^2=(x-3{)}^2(x+4{)}^2$.