Question

Find the LCM of set of polynomials $2t^2+t-3,2t^2+5t+3$.

Short answer

The LCM of given polynomials is $\left(t^2-1\right)\left(2t+3\right)$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $2t^2+t-3,2t^2+5t+3$.

Step 2. Factorize the polynomials and take common factors of each higher power.

The polynomial $2t^2+t-3$ is factorized as: $\left(t-1\right)\left(2t+3\right)$

The polynomial $2t^2+5t+3$ is factorized as: $\left(t+1\right)\left(2t+3\right)$

Taking common factors of each higher power, the LCM of given polynomials is written as:

$\begin{array}{l}LCM=\left(t-1\right)\left(2t+3\right)\left(t+1\right)\\ =\left(t^2-1\right)\left(2t+3\right)\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $\left(t^2-1\right)\left(2t+3\right)$.