Question

Find the lcm of following expressions x²-3x+2and x⁴+x³‐6x²













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Answer 1

Answer:

L.C.M = = x^2(x−1)(x−2)(x−3).

Step-by-step explanation:

x^2 −3x+2 and x^4 +x^3 −6x^2

x^2 −3x+2 can be written as,

→ x^2 -2x -x +2

→ x(x -2) -1(x -2)

→(x-1)(x-2)-----(i)

x^4 +x^3 −6x^2 can be written as,

→ x^2(x^2 + x -6)

→ x^2(x^2 +3x -2x -6)

→ x^2[ x(x +3) -2(x +3) ]

→ x^2[(x -2)(x +3)]---------(ii)

Product of highest power of all the prime factors obtained from equation (i) and (ii)

= x^2(x−1)(x−2)(x+3)

Hence, required L.C.M

= x^2(x−1)(x−2)(x−3).

Answer 2

Answer:

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