Question

lcm of polynomial(x3-x2-2x) and (x3+x2)

Answer 1

Answer:

LCM of x³ - x² -2x and  x³ +x² = x² + x

Step-by-step explanation:

Given polynomials are x³ - x² -2x and  x³ +x²

Required to find the LCM of x³ - x² -2x and  x³ +x²

Solution:

To find LCM we need to factorize the two polynomials

x³ - x² -2x =  x(x² -x -2)

= x(x² - 2x +x -2)

=x(x(x-2)+1(x-2))

=x(x-2)(x+1)

x³ - x² -2x = x(x-2)(x+1)

∴ The factors of x³ -x² -2x  are x, x-2, x+1

x³ + x² = x² (x+1)

∴ The factors of x³ + x² are x,x,x+1

The common factors of x³ - x² -2x and  x³ +x²  are x,x+1

The largest common factors(LCM) of x³ - x² -2x and  x³ +x² is x(x+1)

= x² + x

LCM of x³ - x² -2x and  x³ +x² = x² + x

#SPJ3

Answer 2

Answer:

LCM of (x3-x2-2x ) and (x3+x2) = x2 + x ( x² + x )

Step-by-step explanation:

x3-x2-2x = x( x² - x - 2 )

               = x(x² - 2x +x -2)

               = x[x(x-2) + 1(x -2)]

               = x[(x+1)(x-2)]

x3-x2-2x = x(x+1)(x-2)

Factors of x3-x2-2x  = x , x+1 , x-2

x3+x2 = x²(x+1)

Factors of x3+x2 = x²(x,x) , (x+1)

common factors = x , (x+1)

hence LCM = x(x+1)\

LCM of (x3-x2-2x ) and (x3+x2) = x2 + x ( x² + x )

#SPJ3