Question

Find the LCM of the pair of polynomials.4x² - 9 and 4x² + 12x +9

Answer 1

We need to find the Least Common Multiple between 4x² - 9 and 4x² + 12x +9.

First, we need to factorize each expression:

4x² - 9 can be factorized using the difference of squares given by:

`a^2-b^2=(a+b)(a-b)`

Then:

`4x²-9=(2x+3)(2x-3)`

Now, for 4x² + 12x +9

Can be factorized using:

`(a+b)^2=a^2+2ab+b^2`

Then:

`4x²+12x+9=(2x+3)^2`

Now, we need to find the LCM between (2x+3)(2x-3) and (2x+3)².

Then, the LCM is (2x+3)²(2x-3).

The correct answer is the third option.