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

Accepted Solution

Answer:(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+24Two numbers that when added give -10 but when multiplied give 24will be, -4 and -6Thus the expression becomes:x²-4x-6x+24x(x-4)-6(x-4)=(x-4)(x-6)Let us factorize the second expression.x²-x-12Two numbers when added give -1 and when multiplied give -12are 3 and -4Thus the expression becomes: x²-4x+3x-12x(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