Question

find lcm of polynomials 12(x-1)³ and 15(x-1)(x+2)²​

Answer 1

Answer:

lcm of polynomial=3×2×5(x-1)^3(x+2) ^2

Step-by-step explanation:

12(x-1)^3=3×2×2×(x-1)(x-1)^2===>>1

15(x-1)(x+2)^2=3×5×(x-1)(x+2)^2===>>2

from one and 2

see the common factor =3×2^2×5(x-1)^3(x+2) ^2

Answer 2

Answer:

L.C.M of polynomials 12(x-1)³ and 15(x-1)(x+2)² is 60× (x-1)³× (x+2)².

Step-by-step explanation:

• L.C.M. means the lowest common multiple.
• To determine the L.C.M of the polynomial, first we have to factorise the polynomials.
• Then product of each factor of highest number ( highest times) will be the L.C.M.

factors of 12 (x-1)³:

• 12(x-1)³ can be written as
• $= 2 \times 2 \times 3 \times (x - 1) \times (x - 1) \times (x - 1)$

factors of 15 (x-1) (x+2)²:

• 15 (x-1) (x+2)² can be written as
• $=3 \times 5 \times (x - 1) \times (x + 2) \times (x + 2)$
• We can see that, 2 is two times, 3 one time, 5 one time, (x-1) is three times and (x+2) is two time present.
• So the L.C.M. will be the highest number of the each factor .
• So L.C.M. of the polynomials 12(x-1)³ and 15(x-1)(x+2)² is

$2 \times 2 \times 3 \times 5\times (x - 1) \times (x - 1) \times( x - 1) \times (x + 2) \times (x + 2)$

• $= 60 \times {(x - 1)}^{3} \times {(x + 2)}^{2}$

Conclusion:

L.C.M. of the polynomials 12(x-1)³ and 15(x-1)(x+2)² is 60× (x-1)³× (x+2)².

For more information following links are provided:

https://brainly.in/question/45482448?

https://brainly.in/question/12503894?