Question

Find H. C. F and L. C. M of
x⁴-8x,x³-x²,x³-4x​

Answer 1

H.C.F. = x(x - 2)

L.C.M. is x(x - 1)(x + 2)(x - 2)(x² + 2x + 4).

Step-by-step explanation:

To find the H.C.F. and L.C.M. of the given polynomials, we can factor each of them and then find the highest common factor and lowest common multiple of the factors.

• Factorizing x⁴ - 8x:

x⁴ - 8x = x(x³ - 8) = x(x - 2)(x² + 2x + 4)

• Factorizing x³ - x²:

x³ - x² = x²(x - 1)

• Factorizing x³ - 4x:

x³ - 4x = x(x² - 4) = x(x - 2)(x + 2)

Now we can find the highest common factor by taking the product of the common factors raised to the lowest power. The common factors are x and (x - 2):

H.C.F. = x(x - 2)

To find the lowest common multiple, we take the product of all the factors raised to their highest power. The factors are x, x - 1, x + 2, x - 2, x² + 2x + 4:

L.C.M. = x(x - 1)(x + 2)(x - 2)(x² + 2x + 4)

Therefore, the H.C.F. of the polynomials x⁴ - 8x, x³ - x², x³ - 4x is x(x - 2), and the L.C.M. is x(x - 1)(x + 2)(x - 2)(x² + 2x + 4).