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.
[tex] 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)\\ [/tex]
[tex] 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)\\ [/tex]
Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).
