Question

If $10lm$ is one of the factors of $20l^{2}m+30alm$, find the other factor.

• A. 5l+3m
• B. 2l+3a
• C. 3l+2m
• D. 3l+2a

Answer 1

The correct option is B

2l+3a

The expression $20l^{2}m+30alm$ can be written as

$(2\times 2\times 5\times l\times l\times m)+(2\times 3\times 5\times a\times l\times m)$ .....(i)

Taking out the common factors from expression (i), we get

=$(2\times 5\times l\times m)\left[\right(2\times l)+(3\times a\left)\right]$

= $10lm(2l+3a)$

Therefore, factors of $20l^{2}m+30alm$ are $10lm$ and $2l+3a$.

i.e., $20l^{2}m+30alm$ = $10lm(2l+3a)$

Since it is given that $10lm$ is one factor, then the other factor is $2l+3a$.