Question

Factorise 12 (4x-1/4x)^-5 (4x-1/4x)-2

Answer 1

Answer:

Step-by-step explanation:

Input:

(12 (4 x - 1/4 x))/(4 x - 1/4 x)^5 - 2

Result:

1024/(16875 x^4) - 2

Plots:

Plots

Plots

Alternate forms:

-(2 (16875 x^4 - 512))/(16875 x^4)

(2 (512 - 16875 x^4))/(16875 x^4)

Real roots:

x = -(4 2^(1/4))/(5 3^(3/4))

x = (4 2^(1/4))/(5 3^(3/4))

Complex roots:

x = -(4 i 2^(1/4))/(5 3^(3/4))

x = (4 i 2^(1/4))/(5 3^(3/4))

Roots in the complex plane:

Roots in the complex plane

Properties as a real function:

Domain

{x element R : x!=0}

Range

{y element R : y>-2}

Parity

even

Derivative:

d/dx((12 (4 x - x/4))/(4 x - x/4)^5 - 2) = -4096/(16875 x^5)

Indefinite integral:

integral(-2 + 1024/(16875 x^4)) dx = -1024/(50625 x^3) - 2 x + constant

Limit:

lim_(x-> ± ∞) (-2 + 1024/(16875 x^4)) = -2

Series representations:

-2 + 1024/(16875 x^4) = -32726/16875 + sum_(n=1)^∞ ((-1 + x)^n 512 ((-1)^n (1 + n) (2 + n) (3 + n)))/50625

-2 + 1024/(16875 x^4) = sum_(n=-∞)^∞ ( piecewise | -2 | n = 0

1024/16875 | n = -4) x^n

Answer 2

Answer:

the answer is (45x+8) • (15x-1)