Question

enter the correct answer in the box. find the lcm of these two expressions: ( m^2 + 11m + 10 ) and ( m^2 + 9m - 10 ).

Explanation:

Step1: Factor first quadratic

Factor $m^2 + 11m + 10$ by finding two numbers that multiply to 10 and add to 11.
$m^2 + 11m + 10 = (m + 1)(m + 10)$

Step2: Factor second quadratic

Factor $m^2 + 9m - 10$ by finding two numbers that multiply to -10 and add to 9.
$m^2 + 9m - 10 = (m - 1)(m + 10)$

Step3: Identify unique factors

List all distinct factors from both expressions: $(m-1)$, $(m+1)$, $(m+10)$.

Step4: Compute LCM

Multiply the unique factors together.
$\text{LCM} = (m - 1)(m + 1)(m + 10)$

Step5: Expand (optional, simplified form)

Multiply the factors to get expanded polynomial:
First multiply $(m-1)(m+1) = m^2 - 1$, then multiply by $(m+10)$:
$(m^2 - 1)(m + 10) = m^3 + 10m^2 - m - 10$

Answer:

$(m - 1)(m + 1)(m + 10)$ or $m^3 + 10m^2 - m - 10$