Identify the least common multiple of x2 - 10x + 24 and x2 - x - 12.

(x-4) (x-6) (x+3) or in more compressed form x³-7x²-6x+72

Step-by-step explanation:

To find the L. C. M, w first factorize each of the expressions.

x²-10x+24

Two numbers that when added give - 10 but when multiplied give 24

will be, - 4 and - 6

Thus the expression becomes:

x²-4x-6x+24

x (x-4) - 6 (x-4)

= (x-4) (x-6)

Let us factorize the second expression.

x²-x-12

Two numbers when added give - 1 and when multiplied give - 12

are 3 and - 4

Thus the expression becomes: x²-4x+3x-12

x (x-4) + 3 (x-4)

(x-4) (x+3)

Therefore the LCM between (x-4) (x-6) and (x-4) (x+3)

will be

(x-4) (x-6) (x+3)

We can multiply the expression as follows.

(x-4) (x-6)

x²-6x-4x+24 = x²-10x+24

(x+3) (x²-10x+24)

=x³-10x²+24x+3x²-30x+72

=x³-7x²+-6x+72