What is factor x^4-25x^2+4x^3-100x+3x^2-75 ?

The solution to factor x^4-25x^2+4x^3-100x+3x^2-75 is (x+1)(x+3)(x+5)(x-5)

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factor x^4-25x^2+4x^3-100x+3x^2-75

factor

x^{4} - 25 x^{2} + 4 x^{3} - 100 x + 3 x^{2} - 75

(x + 1) (x + 3) (x + 5) (x - 5)

Solution steps

x^{4} - 25 x^{2} + 4 x^{3} - 100 x + 3 x^{2} - 75

Add similar elements:

- 25 x^{2} + 3 x^{2} = - 22 x^{2}

= x^{4} - 22 x^{2} + 4 x^{3} - 100 x - 75

Write in the standard form

= x^{4} + 4 x^{3} - 22 x^{2} - 100 x - 75

Use the rational root theorem

= (x + 1) \frac{x ^{4} + 4 x ^{3} - 22 x ^{2} - 100 x - 75}{x + 1}

\frac{x ^{4} + 4 x ^{3} - 22 x ^{2} - 100 x - 75}{x + 1} = x^{3} + 3 x^{2} - 25 x - 75

= (x + 1) (x^{3} + 3 x^{2} - 25 x - 75)

Factor

x^{3} + 3 x^{2} - 25 x - 75 : (x + 3) (x + 5) (x - 5)

= (x + 1) (x + 3) (x + 5) (x - 5)

(3 x - 5)^{2} = 21

\frac{2 x - 1}{3} - \frac{5 x - 6}{6} = - 2

- \frac{1}{2} + \frac{1}{3}

\frac{∣ x - 1 ∣}{∣ x + 1 ∣} < 1

14 x^{2} + 13 x - 12

What is factor x^4-25x^2+4x^3-100x+3x^2-75 ?
The solution to factor x^4-25x^2+4x^3-100x+3x^2-75 is (x+1)(x+3)(x+5)(x-5)