Q20.

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

Verified

Answer

The LCM of given polynomials is $(t^{2} - 1) (2 t + 3)$ .

1Step 1. Write down the given polynomials.

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

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

The polynomial $2 t^{2} + t - 3$ is factorized as: $(t - 1) (2 t + 3)$

The polynomial $2 t^{2} + 5 t + 3$ is factorized as: $(t + 1) (2 t + 3)$

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

$\begin{array}{l} L C M = (t - 1) (2 t + 3) (t + 1) \\ = (t^{2} - 1) (2 t + 3) \end{array}$

3Step 3. Conclusion.

The LCM of given polynomials is $(t^{2} - 1) (2 t + 3)$ .