Question

Find the least common multiple of x² + x – 12 and x² + 2x – 15.

Answer 1

Answer:

Least common multiple (x-3) ( x+5) (x +4 ).

Step-by-step explanation:

Given :  x² + x – 12 and x² + 2x – 15.

To find : Find the least common multiple.

Solution : We have given that : x² + x – 12 and x² + 2x – 15.

First : x² + x – 12

On factoring x² + 4x-3x – 12.

Taking common x (x +4 ) -3( x+4 )

(x -3 ) (x +4 )

For : x² + 5x -3x  – 15.

Taking common x (x+5) -3( x +5)

(x-3) ( x+5)

Therefore, Least common multiple (x-3) ( x+5)(x +4 ).

Answer 2

Solution:

we have been asked to find the Least Common multiple of the given polynomial x² + x – 12 and x² + 2x – 15.

To find the least common multiple. Lets first find the factors.

$x^2+x-12=x^2+4x-3x-12\\ \\ x^2+x-12=x(x+4)-3(x+4)\\ \\ x^2+x-12=(x+4)(x-3)$

$x^2+2x-15=x^2+5x-3x-15\\ \\ x^2+2x-15=x(x+5)-3(x+5)\\ \\ x^2+2x-15=(x+5)(x-3)$

Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).