What is factor 32x^5-200x^3+4x^2-25 ?

The solution to factor 32x^5-200x^3+4x^2-25 is (2x+5)(2x-5)(2x+1)(4x^2-2x+1)

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factor 32x^5-200x^3+4x^2-25

factor

32 x^{5} - 200 x^{3} + 4 x^{2} - 25

(2 x + 5) (2 x - 5) (2 x + 1) (4 x^{2} - 2 x + 1)

Solution steps

32 x^{5} - 200 x^{3} + 4 x^{2} - 25

= (32 x^{5} - 200 x^{3}) + (4 x^{2} - 25)

Factor out

8 x^{3}

from

32 x^{5} - 200 x^{3} : 8 x^{3} (4 x^{2} - 25)

= 8 x^{3} (4 x^{2} - 25) + (4 x^{2} - 25)

Factor out common term

(4 x^{2} - 25) : (4 x^{2} - 25) (8 x^{3} + 1)

= (4 x^{2} - 25) (8 x^{3} + 1)

Factor

4 x^{2} - 25 : (2 x + 5) (2 x - 5)

= (2 x + 5) (2 x - 5) (8 x^{3} + 1)

Factor

8 x^{3} + 1 : (2 x + 1) (2^{2} x^{2} - 2 x + 1)

= (2 x + 5) (2 x - 5) (2 x + 1) (2^{2} x^{2} - 2 x + 1)

2^{2} = 4

= (2 x + 5) (2 x - 5) (2 x + 1) (4 x^{2} - 2 x + 1)

5 x^{2} + 7 x - 1 = 0

x^{2} - 8 x + 10 = 0

7 x^{2} + 6 = 0

5 x + 7 = 12

∣ 2 x - 5 ∣ \leq 9

What is factor 32x^5-200x^3+4x^2-25 ?
The solution to factor 32x^5-200x^3+4x^2-25 is (2x+5)(2x-5)(2x+1)(4x^2-2x+1)