What is factor x^5-4x^3+8x^2-32 ?

The solution to factor x^5-4x^3+8x^2-32 is (x+2)^2(x-2)(x^2-2x+4)

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factor x^5-4x^3+8x^2-32

factor

x^{5} - 4 x^{3} + 8 x^{2} - 32

(x + 2)^{2} (x - 2) (x^{2} - 2 x + 4)

Solution steps

x^{5} - 4 x^{3} + 8 x^{2} - 32

= (x^{5} - 4 x^{3}) + (8 x^{2} - 32)

Factor out

x^{3}

from

x^{5} - 4 x^{3} : x^{3} (x^{2} - 4)

Factor out

8

from

8 x^{2} - 32 : 8 (x^{2} - 4)

= x^{3} (x^{2} - 4) + 8 (x^{2} - 4)

Factor out common term

x^{2} - 4

= (x^{2} - 4) (x^{3} + 8)

Factor

x^{2} - 4 : (x + 2) (x - 2)

= (x + 2) (x - 2) (x^{3} + 8)

Factor

x^{3} + 8 : (x + 2) (x^{2} - 2 x + 2^{2})

= (x + 2) (x - 2) (x + 2) (x^{2} - 2 x + 2^{2})

Apply exponent rule:

aa = a^{2}

(x + 2) (x + 2) = (x + 2)^{2}

= (x + 2)^{2} (x - 2) (x^{2} - 2 x + 2^{2})

2^{2} = 4

= (x + 2)^{2} (x - 2) (x^{2} - 2 x + 4)

(4 x - 12) - 2 (4 x - 5) = (11 - 26) x

4 x^{2} - 12 x + 9 = 5

4 n - 2 n = 4

b^{2} + 60 b + 224

- 3 e^{x} + e^{- x}

What is factor x^5-4x^3+8x^2-32 ?
The solution to factor x^5-4x^3+8x^2-32 is (x+2)^2(x-2)(x^2-2x+4)