Question

Find the LCM of x^2 - 16 and 2 x ^2 - 9 x + 4

Answer 1

LCM, is the smallest positive integer that is divisible by both a and b.

LCM is =(x+4)(x-4)(2x-1)

see above attachment ✔️

Hope it helps you ❣️☑️

Answer 2

Answer:

To find LCM of both polynomials firstly we have to express both in their factor form as:-)

${x}^{2} - 16 \\ \\ = {x}^{2} - {4}^{2} \\ \\ = ( x+ 4)(x - 4)$

And

$\: \: \: \: 2 {x}^{2} - 9x + 4 \\ \\ = 2 {x}^{2} - 8x - x + 4 \\ \\ = 2x(x - 4) - 1(x - 4) \\ \\ = (x - 4)(2x - 1)$

Now,

we can find LCM by taking common factors.

So, using above expressions

LCM will be

$(x + 4) \times (x - 4) \times (2x - 1) \\ \\ = 2 {x}^{3} + {x}^{2} - 32x - 16$