What is factor x^4-5x^3+4x^2-16x^2+80x-64 ?

The solution to factor x^4-5x^3+4x^2-16x^2+80x-64 is (x-1)(x-4)^2(x+4)

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factor x^4-5x^3+4x^2-16x^2+80x-64

factor

x^{4} - 5 x^{3} + 4 x^{2} - 16 x^{2} + 80 x - 64

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

Solution steps

x^{4} - 5 x^{3} + 4 x^{2} - 16 x^{2} + 80 x - 64

Add similar elements:

4 x^{2} - 16 x^{2} = - 12 x^{2}

= x^{4} - 5 x^{3} - 12 x^{2} + 80 x - 64

Use the rational root theorem

= (x - 1) \frac{x ^{4} - 5 x ^{3} - 12 x ^{2} + 80 x - 64}{x - 1}

\frac{x ^{4} - 5 x ^{3} - 12 x ^{2} + 80 x - 64}{x - 1} = x^{3} - 4 x^{2} - 16 x + 64

= (x - 1) (x^{3} - 4 x^{2} - 16 x + 64)

Factor

x^{3} - 4 x^{2} - 16 x + 64 : (x - 4) (x + 4) (x - 4)

= (x - 1) (x - 4) (x + 4) (x - 4)

Apply exponent rule:

aa = a^{2}

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

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

(x^{3})^{\frac{8}{15}}

x^{4} + 4 x^{3} - 9 x^{2} - 16 x + 20

- x^{2} + 8 x - 12

x^{2} + 4 x \leq 0

4 x^{2} - 40 x + 100 = 0

What is factor x^4-5x^3+4x^2-16x^2+80x-64 ?
The solution to factor x^4-5x^3+4x^2-16x^2+80x-64 is (x-1)(x-4)^2(x+4)